eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2017-10-01
08
1
1
21
10.22130/scma.2017.23646
23646
مقاله پژوهشی
$G$-Frames for operators in Hilbert spaces
Bahram Dastourian
bdastorian@gmail.com
1
Mohammad Janfada
janfada@um.ac.ir
2
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, P.O. Box 1159-91775, Iran.
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, P.O. Box 1159-91775, Iran.
$K$-frames as a generalization of frames were introduced by L. Gu{a}vruc{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.
http://scma.maragheh.ac.ir/article_23646_5b6f187d7a7e622a7634cf56284bc2c6.pdf
$g$-atomic system
$g$-$K$-frame
$g$-$K$-dual
Perturbation
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2017-10-01
08
1
23
32
10.22130/scma.2017.22636
22636
مقاله پژوهشی
Generalized Ritt type and generalized Ritt weak type connected growth properties of entire functions represented by vector valued Dirichlet series
Sanjib Kumar Datta
sanjib_kr_datta@yahoo.co.in
1
Tanmay Biswas
tanmaybiswas_math@rediffmail.com
2
Jinarul Haque Shaikh
jnrlhqshkh188@gmail.com
3
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN- 741235, West Bengal, India.
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.
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.
http://scma.maragheh.ac.ir/article_22636_d44441b3c78ee5e56778a0617e77ab53.pdf
Vector valued Dirichlet series (VVDS)
Generalized Ritt order
Generalized Ritt lower order
Generalized Ritt-type
Generalized Ritt weak type
growth
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2017-10-01
08
1
33
41
10.22130/scma.2017.23072
23072
مقاله پژوهشی
Second dual space of little $alpha$-Lipschitz vector-valued operator algebras
Abbasali Shokri
a-shokri@iau-ahar.ac.ir
1
Department of Mathematics, Ahar Branch, Islamic Azad University, Ahar, Iran.
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.
http://scma.maragheh.ac.ir/article_23072_37fba52745f4bc2b7c6107415e1dffc2.pdf
Second dual space
$alpha$-Lipschitz operator
Vector-valued operator
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2017-10-01
08
1
43
53
10.22130/scma.2017.23337
23337
مقاله پژوهشی
Generated topology on infinite sets by ultrafilters
Alireza Bagheri Salec
alireza_bagheri_salec@yahoo.com
1
Department of Mathematics, Faculty of Science, University of Qom, P.O.Box 3716146611, Qom, Iran.
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.
http://scma.maragheh.ac.ir/article_23337_6c78346b95a2ee9f22a0f2d5078a421e.pdf
Stone-$check{C}$ech compactification
Axiom of separation
Filter
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2017-10-01
08
1
55
71
10.22130/scma.2017.22045
22045
مقاله پژوهشی
Contra $beta^{*}$-continuous and almost contra $beta^{*}$-continuous functions
Appachi Vadivel
avmaths@gmail.com
1
Radhakrishnan Ramesh
rameshroshitha@gmail.com
2
Duraisamy Sivakumar
sivakumardmaths@yahoo.com
3
Department of Mathematics, Annamalai University, Annamalai Nagar-608 002, Tamil Nadu, India.
Department of Mathematics, Pope John Paul II College of Education, Reddiar Palayam, Puducherry-605010, India.
Department of Mathematics (DDE), Annamalai University, Annamalai Nagar-608 002, Tamil Nadu, India.
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.
http://scma.maragheh.ac.ir/article_22045_9b9885af1b47833c61470ac4706d0a25.pdf
$beta^{*}$-closed sets
Contra $beta^{*}$-continuous
Almost contra $beta^{*}$-continuous functions
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2017-10-01
08
1
73
81
10.22130/scma.2017.22852
22852
مقاله پژوهشی
Stability of additive functional equation on discrete quantum semigroups
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.
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.
http://scma.maragheh.ac.ir/article_22852_a21e351c5081462f3ee9b1f99cdd027a.pdf
Discrete quantum semigroup
Additive functional equation
Hyers-Ulam stability
Noncommutative geometry
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2017-10-01
08
1
83
96
10.22130/scma.2017.22412
22412
مقاله پژوهشی
Compare and contrast between duals of fusion and discrete frames
Elnaz Osgooei
e.osgooei@uut.ac.ir
1
Ali akbar Arefijammal
arefijamaal@gmail.com
2
Department of Sciences, Urmia University of Technology, P.O.Box 419-57155, Urmia, Iran.
Department of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O.Box 397, Sabzevar, Iran.
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.
http://scma.maragheh.ac.ir/article_22412_6e582d16caaf2352781eab207dfc817c.pdf
Frames
fusion frames
dual fusion frames
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2017-10-01
08
1
97
106
10.22130/scma.2017.23850
23850
مقاله پژوهشی
Subspace-diskcyclic sequences of linear operators
Mohammad Reza Azimi
mhr.azimi@maragheh.ac.ir
1
Department of Mathematics, Faculty of Sciences, University of Maragheh, Maragheh, Iran.
A sequence ${T_n}_{n=1}^{infty}$ of bounded linear operators on a separable infinite dimensional Hilbert space<br /> $mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $Msubseteq mathcal{H},$ if there exists a vector $xin mathcal{H}$ such that the disk-scaled orbit ${alpha T_n x: nin mathbb{N}, alpha inmathbb{C}, | alpha | leq 1}cap M$ 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).
http://scma.maragheh.ac.ir/article_23850_39a0664f6ddf12b1b192462ffddd7aaf.pdf
Sequences of operators
Diskcyclic vectors
Subspace-diskcyclicity
Subspace-hypercyclicity