ORIGINAL_ARTICLE
$G$-Frames for operators in Hilbert spaces
$K$-frames as a generalization of frames were introduced by L. G\u{a}vru\c{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new generalization of $K$-frames. After proving some characterizations of generalized $K$-frames, new results are investigated and some new perturbation results are established. Finally, we give several characterizations of $K$-duals.
https://scma.maragheh.ac.ir/article_23646_5b6f187d7a7e622a7634cf56284bc2c6.pdf
2017-10-01
1
21
10.22130/scma.2017.23646
$g$-atomic system
$g$-$K$-frame
$g$-$K$-dual
Perturbation
Bahram
Dastourian
bdastorian@gmail.com
1
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, P.O. Box 1159-91775, Iran.
AUTHOR
Mohammad
Janfada
janfada@um.ac.ir
2
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, P.O. Box 1159-91775, Iran.
LEAD_AUTHOR
[1] A. Abdollahi and E. Rahimi, Some results on g-frames in Hilbert spaces, Turk. J. Math., 35 (2011) 695-704.
1
[2] M.R. Abdollahpour, M.H. Faroughi, and A. Rahimi, Pg-frames in Banach spaces, Methods Funct. Anal. Topology, 13 (2007) no. 3, 201-210.
2
[3] A.A. Arefijamaal and S. Ghasemi, On characterization and stability of alternate dual of g-frames, Turk. J. Math., 37 (2013) 71-79.
3
[4] M.S. Asgari and H. Rahimi, Generalized frames for operators in Hilbert spaces, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 17 (2014) no. 2, 1450013 (20 pages).
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[5] H. Bolcskei, F. Hlawatsch and H.G. Feichtinger, Frame-theoretic analyssis of oversampled filter banks, IEEE Trans. Signal Process., 46 (1998) 3256-3268.
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[6] O. Christensen, An Introduction to Frame and Riesz Bases, Birkhäuser, 2002.
6
[7] B. Dastourian and M. Janfada, *-frames for operators on Hilbert modules, Wavelets and Linear algebras., 3 (2016) 27-43.
7
[8] B. Dastourian and M. Janfada, Frames for operators in Banach spaces via semi-inner products, Int. J. Wavelets Multiresult. Inf. Process., 14 (2016) no. 3, 1650011 (17 pages).
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[9] I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27 (1986) 1271-1283.
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[10] R.G. Douglas, On majorization, factorization and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc., 17 (1966) no. 2, 413-415.
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[11] N.E. Dudey Ward and J.R. Partington, A construction of rational wavelets and frames in Hardy-Sobolev space with applications to system modelling, SIAM J. Control Optim., 36 (1998) 654-679.
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[12] J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952) 341-366.
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[13] Y.C. Eldar, Sampling with arbitrary sampling and reconstruction spaces and oblique dual frame vectors, J. Fourier. Anal. Appl., 9 (2003) no. 1, 77-96.
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[14] Y.C. Eldar and T. Werther, General framework for consistent sampling in Hilbert spaces, Int. J. Wavelets Multi. Inf. Process., 3 (2005) no. 3, 347-359.
14
[15] H.G. Feichtinger and T. Werther, Atomic systems for subspaces, in: L. Zayed (Ed.), Proceedings SampTA 2001, Orlando, FL, (2001) 163-165.
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[16] P.J.S.G. Ferreira, Mathematics for multimedia signal processing II: Discrete finite frames and signal reconstruction, In: Byrnes, J.S. (ed.) Signal processing for multimedia, IOS Press, Amsterdam (1999) 35-54.
16
[17] L. Gávruta, Frames for operators, Appl. Comput. Harmon. Anal., 32 (2012) 139-144.
17
[18] A. Khosravi and K. Musazadeh, Fusion frames and g-frames, J. Math. Anal. Appl., 342 (2008) 1068-1083.
18
[19] A. Najati, M.H. Faroughi, and A. Rahimi, G-frames and stability of g-frames in Hilbert space, Methods Funct. Anal. Topology, 14 (2008) 271-286.
19
[20] F.A. Neyshaburi and A.A. Arefijamaal, Some constructions of K-frames and their duals, To appear in Rocky Mountain J. Math.
20
[21] S. Obeidat, S. Samarah, P.G. Casazza, and J. C. Tremain, Sums of Hilbert space frames, J. Math. Anal. Appl., 351 (2009) 579-585.
21
[22] T. Strohmer and R. Jr. Heath, Grassmanian frames with applications to coding and communications, Appl. Comput. Harmon. Anal., 14 (2003) 257-275.
22
[23] W. Sun, g-frames and g-Riesz bases, J. Math. Anal. Appl., 322 (2006) 437–452.
23
[24] Y.J. Wang and Y.C. Zhu, G-Frames and g-Frame sequences in Hilbert spaces, Acta Mathematica Sinica, 25 (2009) no. 12, 2093-2106.
24
[25] X.C. Xiao and X.M. Zeng, Some properties of g-frames in Hilbert C*-modules, J. Math. Anal. Appl., 363 (2010) 399-408.
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[26] X. Xiao, Y. Zhu, and L. Gávruta, Some properties of $K$-frames in Hilbert spaces, Results. Math., 63 (2013) no. 3-4, 1243-1255.
26
[27] X. Xiao, Y. Zhu, Z. Shu, and M. Ding, G-frames with bounded linear operators, Rocky Mountain J. Math., 45 (2015) no. 2, 675-693.
27
ORIGINAL_ARTICLE
Generalized Ritt type and generalized Ritt weak type connected growth properties of entire functions represented by vector valued Dirichlet series
In this paper, we introduce the idea of generalized Ritt type and generalised Ritt weak type of entire functions represented by a vector valued Dirichlet series. Hence, we study some growth properties of two entire functions represented by a vector valued Dirichlet series on the basis of generalized Ritt type and generalised Ritt weak type.
https://scma.maragheh.ac.ir/article_22636_d44441b3c78ee5e56778a0617e77ab53.pdf
2017-10-01
23
32
10.22130/scma.2017.22636
Vector valued Dirichlet series (VVDS)
Generalized Ritt order
Generalized Ritt lower order
Generalized Ritt-type
Generalized Ritt weak type
growth
Sanjib Kumar
Datta
sanjib_kr_datta@yahoo.co.in
1
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN- 741235, West Bengal, India.
LEAD_AUTHOR
Tanmay
Biswas
tanmaybiswas_math@rediffmail.com
2
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.
AUTHOR
Jinarul Haque
Shaikh
jnrlhqshkh188@gmail.com
3
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.
AUTHOR
[1] Q.I. Rahaman, The Ritt order of the derivative of an entire function, Annales Polonici Mathematici, Vol 17 (1965), pp. 137-140.
1
[2] C.T. Rajagopal and A.R. Reddy, A note on entire functions represented by Dirichlet series, Annales Polonici Mathematici, Vol 17 (1965), pp. 199-208.
2
[3] J.F. Ritt, On certain points in the theory of Dirichlet series, Amer. Jour. Math., Vol. 50 (1928), pp. 73-86.
3
[4] D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., Vol. 69 (1963), pp. 411-414.
4
[5] R.P. Srivastav and R.K. Ghosh, On entire functions represented by Dirichlet series, Annales Polonici Mathematici, Vol 13 (1963), pp. 93-100.
5
[6] B.L. Srivastava, A study of spaces of certain classes of vector valued Dirichlet series, Thesis, I. I. T., Kanpur, (1983).
6
[7] G.S. Srivastava and A. Sharma, On generalized order and generalized type of vector valued Dirichlet series of slow growth, Int. J. Math. Archive, Vol. 2, No. 12 (2011), pp. 2652-2659.
7
ORIGINAL_ARTICLE
Second dual space of little $\alpha$-Lipschitz vector-valued operator algebras
Let $(X,d)$ be an infinite compact metric space, let $(B,\parallel . \parallel)$ be a unital Banach space, and take $\alpha \in (0,1).$ In this work, at first we define the big and little $\alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $\alpha$-lipschitz $B$-valued operator algebra, $lip_{\alpha}(X,B)$. Then we characterize its second dual space.
https://scma.maragheh.ac.ir/article_23072_37fba52745f4bc2b7c6107415e1dffc2.pdf
2017-10-01
33
41
10.22130/scma.2017.23072
Second dual space
$alpha$-Lipschitz operator
Vector-valued operator
Abbasali
Shokri
a-shokri@iau-ahar.ac.ir
1
Department of Mathematics, Ahar Branch, Islamic Azad University, Ahar, Iran.
LEAD_AUTHOR
[1] A. Abdollahi, The maximal ideal space of analutic Lipschitz algebras, Rend. Circ. Mat. Palermo(2), 47 (1998), 347-352.
1
[2] D. Alimohammadi and A. Ebadian, Hedberg's theorem in real Lipschitz algebras, Indian J. Pure Appl. Math, 32 (2001), 1479-1493.
2
[3] H.X. Cao and Z.B. Xu, Some properties of Lipschitz-α operators, Acta Mathematica Sinica, Chinese Series, 45(2) (2002), 279-286.
3
[4] H.X. Cao, J.H. Zhang, and Z.B. Xu, Characterizations and Extensions of Lipschitz-α operators, Acta Mathematica Sinica, English Series, 22(3) (2006), 671-678.
4
[5] H.G. Dales, Banach algebras and Automatic Continuty, Clarendon Press. Oxford, 2000.
5
[6] A. Ebadian, Prime ideals in Lipschitz algebras of finite differentiable functions, Honam Math. J., 22 (2000), 21-30.
6
[7] T.G. Honary and H. Mahyar, Approximation in Lipschitz algebras, Quaest. Math., 23 (2000), 13-19.
7
[8] J.A. Johnson, Lipschitz spaces, Pacific J. Math., 51 (1975), 177-186.
8
[9] B. Pavlovic, Automatic continuity of Lipschitz algebras, J. Funct. anal. 131 (1995), 115-144.
9
[10] D.R. Sherbert, Banach algebras of Lipschitz functions, Pacific J. Math. 13 (1963), 1387-1399.
10
[11] N. Waver, Subalgebras of little Lipschitz algebras, Pacific J. Math., 173 (1996), 283-293.
11
ORIGINAL_ARTICLE
Generated topology on infinite sets by ultrafilters
Let $X$ be an infinite set, equipped with a topology $\tau$. In this paper we studied the relationship between $\tau$, and ultrafilters on $X$. We can discovered, among other thing, some relations of the Robinson's compactness theorem, continuity and the separation axioms. It is important also, aspects of communication between mathematical concepts.
https://scma.maragheh.ac.ir/article_23337_6c78346b95a2ee9f22a0f2d5078a421e.pdf
2017-10-01
43
53
10.22130/scma.2017.23337
Stone-$check{C}$ech compactification
Axiom of separation
Filter
Alireza
Bagheri Salec
alireza_bagheri_salec@yahoo.com
1
Department of Mathematics, Faculty of Science, University of Qom, P.O.Box 3716146611, Qom, Iran.
LEAD_AUTHOR
[1] R. Engelking, General Topology, Berlin, Sigma series in pure mathematics, Vol. 6, 1989.
1
[2] N. Hindman and I. Leader, The semigroup of ultrafilters near 0, Semigroup Forum, 59 (1999), 33-55.
2
[3] N. Hindman and D. Strauss, Algebra in the Stone-Cech Compactification, Theory and Application, Springer Series in Computational Mathematics, Walter de Gruyter, Berlin, 1998.
3
[4] M.A. Tootkaboni and T. Vahed, The semigroup of ultrafilters near an idempotent of a semitopological semigroup, Topology and its Applications, Vol 159, Issue 16, (2012), 3494-3503.
4
[5] Y. Zelenyuk, Ultrafilters and Topologies on Groups, Walter de Gruyter, Berlin, 2011.
5
ORIGINAL_ARTICLE
Contra $\beta^{*}$-continuous and almost contra $\beta^{*}$-continuous functions
The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion of $\beta^{*}$-closed sets in topological space to present and study a new class of functions called contra $\beta^{*}$-continuous and almost contra $\beta^{*}$-continuous functions as a new generalization of contra continuity.
https://scma.maragheh.ac.ir/article_22045_9b9885af1b47833c61470ac4706d0a25.pdf
2017-10-01
55
71
10.22130/scma.2017.22045
$beta^{*}$-closed sets
Contra $beta^{*}$-continuous
Almost contra $beta^{*}$-continuous functions
Appachi
Vadivel
avmaths@gmail.com
1
Department of Mathematics, Annamalai University, Annamalai Nagar-608 002, Tamil Nadu, India.
LEAD_AUTHOR
Radhakrishnan
Ramesh
rameshroshitha@gmail.com
2
Department of Mathematics, Pope John Paul II College of Education, Reddiar Palayam, Puducherry-605010, India.
AUTHOR
Duraisamy
Sivakumar
sivakumardmaths@yahoo.com
3
Department of Mathematics (DDE), Annamalai University, Annamalai Nagar-608 002, Tamil Nadu, India.
AUTHOR
[1] K. Al-Zoubi and B. Al-Nashef, The topology of $omega$-open subsets, Al-Manarah Journal, 9 (2) (2003), 169-179.
1
[2] M. Caldas and S. Jafari, Some properties of contra-$beta$-continuous functions, Memoirs of the Faculty of Science Kochi University. Series A. Mathematics, 22 (2001), 19-28.
2
[3] K. Dlaska, N. Ergun, and M. Ganster, Countably $S$-closed spaces, Mathematica Slovaca, 44 (3) (1994), 337-348.
3
[4] K. Dontchev, Contra-continuous functions and strongly $S$-closed spaces, International Journal of Mathematics and Mathematical Sciences, 19 (2) (1996), 303-310.
4
[5] J. Dontchev and T. Noiri, Contra-semicontinuous functions, Mathematica Pannonica, 10 (2) (1999), 159-168.
5
[6] E. Ekici, Almost contra-precontinuous functions, Bulletin of the Malaysian Mathematical Sciences Society, 27 (1) (2004), 53-65.
6
[7] H.Z. Hdeib, $omega$-closed mappings, Revista Colombiana de Matematicas, 16 (1-2) (1982), 65-78.
7
[8] S. Jafari and T. Noiri, On contra-precontinuous functions, Bulletin of the Malaysian Mathematical Sciences Society, 25 (2) (2002), 115-128.
8
[9] S. Jafari and T. Noiri, Contra-$alpha$-continuous functions between topological spaces, Iranian International Journal of Science, 2 2 (2001), 153-167.
9
[10] J.E. Joseph and M.H. Kwack, On $S$-closed spaces, Proceedings of the American Mathematical Society, 80 (2) (1980), 341-348.
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[11] N. Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo, 19 (2) (1920), 89-96.
11
[12] M. Mrsevic, On pairwise $R$ and pairwise $R_1$ bitopological spaces, Bull Math Soc Sci Math $RS$ Roumanie, 30 (1986), 141-148.
12
[13] A.A. Nasef, Some properties of contra-$gamma$-continuous functions, Chaos Solitons and Fractals, 24 (2) (2005), 471-477.
13
[14] T. Noiri and V. Popa, Some properties of almost contra-precontinuous functions, Bulletin of the Malaysian Mathematical Sciences Society, { 28} (2) (2005), 107-116.
14
[15] P.G. Palanimani and R. Parimelazhagan, $beta^{*}$-closed sets in topological spaces, ROSR Journal of Mathematics, 5 (1) (2013), 47-50.
15
[16] R. Ramesh, A. Vadivel, and D. Sivakumar, On $beta^{*}$-connectedness and $beta^{*}$-disconnectedness and thier applications, Journal of advanced research in scientific computing, 7 (1) (2015), 10-18.
16
[17] R. Ramesh, A. Vadivel, and D. Sivakumar, $beta^{*}$-regular and $beta^{*}$-normal spaces, Int. J. of Pure and Engg. Mathematics, 2 (III) (2014), 78-80.
17
[18] R. Ramesh, A. Vadivel, and D. Sivakumar, Properties of $beta^{*}$-homeomorphisms in topological spaces, Gen. Math. Notes, 26 (1) (2015), 1-7.
18
[19] M.K. Singal and A. Mathur, On nearly-compact spaces, Bollettino della Unione Matematica Italiana, 2 (1969), 702-710.
19
[20] T. Soundararajan, Weakly Hausdorff spaces and the cardinality of topological spaces in General Topology and Its Relations to Modern Analysis and Algebra, III (Proc. Conf., Kanpur, 1968), Academia, Prague, 1971, 301-306.
20
ORIGINAL_ARTICLE
Stability of additive functional equation on discrete quantum semigroups
We construct a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result generalizes a famous and old result due to Forti on the Hyers-Ulam stability of additive functional equations on amenable classical discrete semigroups.
https://scma.maragheh.ac.ir/article_22852_a21e351c5081462f3ee9b1f99cdd027a.pdf
2017-10-01
73
81
10.22130/scma.2017.22852
Discrete quantum semigroup
Additive functional equation
Hyers-Ulam stability
Noncommutative geometry
Maysam
Maysami Sadr
sadr@iasbs.ac.ir
1
Department of Mathematics, Institute for Advanced Studies in Basic Sciences, P.O.Box 45195-1159, Zanjan 45137-66731, Iran.
LEAD_AUTHOR
[1] E. Bèdos, G.J. Murphy, and L. Tuset, Amenability and co-amenability of algebraic quantum groups, Int. J. Math. Math. Sci., 31 (2002) 577-601.
1
[2] M-E. Craioveanu, M. Puta, and Th.M. Rassias, Old and New Aspects in Spectral Geometry, Kluwer Academic Publishers, Dordrecht, Boston, London, 2001.
2
[3] E.G. Effros and Z.-J. Ruan, Discrete quantum groups $I$, the Haar measure, Int. J. Math., 5 (1994) 681-723.
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[4] M. Enock and J.-M. Schwartz, Kac algebras and duality of locally compact groups, Springer-Verlag, Berlin-Heidelberg-New York, 1992.
4
[5] G.L. Forti, The stability of homomorphisms and amenability, with applications to functional equations, Abh. Math. Sem. Univ. Hamburg, 57 (1987) 215-226.
5
[6] D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 27 (1941) 222-224.
6
[7] S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer Optimization and Its Applications, New York, 2011.
7
[8] J. Kustermans and S. Vaes, Locally compact quantum groups, Ann. Sci. École Norm. Sup., (4) 33 (2000) 837-934.
8
[9] C. Mortici, M.Th. Rassias, and S.-M. Jung, On the stability of a functional equation associated with the Fibonacci numbers, Abstract and Applied Analysis, Hindawi Publishing Corporation, Volume 2014 (2014),Article ID 546046, 6 pages.
9
[10] A. Pràstaro and Th.M. Rassias, On Ulam stability in the geometry of PDEs, In: Functional Equations, Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, Boston, London, 2003, pp. 139-147.
10
[11] S.M. Ulam, A Collection of the Mathematical Problems, Interscience Publ., New York, 1960.
11
[12] A. Van Daele, Discrete quantum groups, J. Algebra, 180 (1996) 431-444.
12
ORIGINAL_ARTICLE
Compare and contrast between duals of fusion and discrete frames
Fusion frames are valuable generalizations of discrete frames. Most concepts of fusion frames are shared by discrete frames. However, the dual setting is so complicated. In particular, unlike discrete frames, two fusion frames are not dual of each other in general. In this paper, we investigate the structure of the duals of fusion frames and discuss the relation between the duals of fusion frames with their associated discrete frames.
https://scma.maragheh.ac.ir/article_22412_6e582d16caaf2352781eab207dfc817c.pdf
2017-10-01
83
96
10.22130/scma.2017.22412
Frames
fusion frames
dual fusion frames
Elnaz
Osgooei
e.osgooei@uut.ac.ir
1
Department of Sciences, Urmia University of Technology, P.O.Box 419-57155, Urmia, Iran.
AUTHOR
Ali akbar
Arefijammal
arefijamaal@gmail.com
2
Department of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O.Box 397, Sabzevar, Iran.
LEAD_AUTHOR
[1] Z. Amiri, M.A. Dehghan, and E. Rahimi, Subfusion frames, Abstr. Appl. Anal., 2012 (2012) 1-12.
1
[2] A. Arefijamaal and S. Ghasemi, On characterization and stability of alternate dual of g-frames, Turk. J. Math., 37 (2013) 71-79.
2
[3] A. Arefijamaal, E. Zekaee, Image processing by alternate dual Gabor frames, To appear in Bull. Iranian Math. Soc.
3
[4] A. Arefijamaal and E. Zekaee, Signal processing by alternate dual Gabor frames, Appl. Comput. Harmon. Anal., 35 (2013) 535-540.
4
[5] R. Calderbank, P.G. Casazza, A. Heinecke, G. Kutyniok, and A. Pezeshki, Sparse fusion frames: existence and construction, Adv. Comput. Math., 35 (1) (2011) 1-31.
5
[6] P.G. Casazza and M. Fickus, Minimizing fusion frame potential, Acta, Appl. Math., 107 (2009) 7-24.
6
[7] P.G. Casazza and G. Kutyniok, Frames of subspaces, Contemp. Math., vol. 345, Amer. Math. Soc., Providence, RI, (2004) 87-113.
7
[8] P.G. Casazza, G. Kutyniok, and S. Li, Fusion frames and distributed processing, Appl. Comput. Harmon. Anal., 25 (1) (2008) 114-132.
8
[9] O. Christensen, Frames and Bases: An Introductory Course, Birkhäuser, Boston, 2008.
9
[10] O. Christensen and E. Osgooei, On frame properties for Fourier-like systems, J. Approx. Theory, 172 (2013) 47-57.
10
[11] M.A. Dehghan and M.A. Hasankhani Fard, G-dual frames in Hilbert spaces, U. P. B. Sci. Bull. Series A, 75 (1) (2013) 129-140.
11
[12] P. Gavruta, On the duality of fusion frames, J. Math. Anal. Appl., 333 ( 2) (2007) 871-879.
12
[13] W.H. Greub, Linear Algebra, Springer-Verlag, New York, 1981.
13
[14] S.K. Kaushik, A generalization of frames in Banach spaces, J. Contemp. Math. Anal., 44 (4) (2009) 212-218.
14
[15] J. Leng, Q. Guo, and T. Huang, The duals of fusion frames for experimental data transmission coding of high energy physics, Adv. High Energy Phys., 2013 (2013) 1-9.
15
[16] P.G. Massey, M.A. Ruiz, and D. Stojanoff, The structure of minimizers of the frame potential on fusion frames, J. Fourier Anal. Appl., 16 (2010) 514-543.
16
[17] A. Najati, A. Rahimi, and M.H. Faroughi, Continuous and discrete frames of subspaces in Hilbert spaces, Southeast Asian Bull. Math., 32 (2008) 305-324.
17
[18] E. Osgooei and M.H. Faroughi, Hilbert-Schmidt sequences and dual of g-frames, Acta Univ. Apulensis, 36 (2013) 1-15.
18
[19] A. Rahimi, Invariance of Fréchet frames under perturbation, Sahand Communications in Mathematical Analysis, 1 (1) (2014), 41-51.
19
ORIGINAL_ARTICLE
Subspace-diskcyclic sequences of linear operators
A sequence $\{T_n\}_{n=1}^{\infty}$ of bounded linear operators on a separable infinite dimensional Hilbert space $\mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $M\subseteq \mathcal{H},$ if there exists a vector $x\in \mathcal{H}$ such that the disk-scaled orbit $\{\alpha T_n x: n\in \mathbb{N}, \alpha \in\mathbb{C}, | \alpha | \leq 1\}\cap M$ is dense in $M$. The goal of this paper is the studying of subspace diskcyclic sequence of operators like as the well known results in a single operator case. In the first section of this paper, we study some conditions that imply the diskcyclicity of $\{T_n\}_{n=1}^{\infty}$. In the second section, we survey some conditions and subspace-diskcyclicity criterion (analogue the results obtained by some authors in \cite{MR1111569, MR2261697, MR2720700}) which are sufficient for the sequence $\{T_n\}_{n=1}^{\infty}$ to be subspace-diskcyclic(subspace-hypercyclic).
https://scma.maragheh.ac.ir/article_23850_39a0664f6ddf12b1b192462ffddd7aaf.pdf
2017-10-01
97
106
10.22130/scma.2017.23850
Sequences of operators
Diskcyclic vectors
Subspace-diskcyclicity
Subspace-hypercyclicity
Mohammad Reza
Azimi
mhr.azimi@maragheh.ac.ir
1
Department of Mathematics, Faculty of Sciences, University of Maragheh, Maragheh, Iran.
LEAD_AUTHOR
[1] N. Bamerni, V. Kadets, and A. Kιlιçman, On subspaces diskcyclicity, arXiv:1402.4682 [math.FA], 1-11.
1
[2] N. Bamerni, V. Kadets, A. Kιlιçman, and M.S.M. Noorani, A review of some works in the theory of diskcyclic operators, Bull. Malays. Math. Sci. Soc., Vol. 39 (2016) 723-739.
2
[3] F. Bayart and ´E. Matheron, Dynamics of linear operators, Cambridge Tracts in Mathematics, Vol. 179, Cambridge University Press, Cambridge, 2009.
3
[4] L. Bernal-Gonz´alez and K.-G. Grosse-Erdmann, The hypercyclicity criterion for sequences of operators, Studia Math., Vol. 157 No. 1 (2003) 17-32.
4
[5] P.S. Bourdon, Invariant manifolds of hypercyclic vectors, Proc. Amer. Math. Soc., Vol. 118 No. 3 (1993) 845-847.
5
[6] G. Godefroy and J.H. Shapiro, Operators with dense, invariant, cyclic vector manifolds, J. Funct. Anal., Vol. 98 No. 2 (1991) 229-269.
6
[7] K-G. Grosse-Erdmann, Universal families and hypercyclic operators, Bull. Amer. Math. Soc., Vol. 36 No. 3 (1999) 345-381.
7
[8] R.R. Jiménez-Munguía, R.A. Martínez-Avendaño, and A. Peris, Some questions about subspace-hypercyclic operators, J. Math. Anal. Appl., Vol. 408 No. 1 (2013) 209-212.
8
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9
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