eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-01-01
09
1
1
14
10.22130/scma.2018.24240
24240
مقاله پژوهشی
Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions
Maliheh Mayghani
m_maighany@yahoo.com
1
Davood Alimohammadi
alimohammadi.davood@gmail.com
2
Department of Mathematics, Payame Noor University, P. O. Box: 19359-3697, Tehran, Iran.
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran.
We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we prove that every unital endomorphism of real Lipschitz algebras of complex-valued functions on compact metric spaces with Lipschitz involutions is a composition operator. Finally, we study some properties of quasicompact and Riesz unital endomorphisms of these algebras.
http://scma.maragheh.ac.ir/article_24240_91e55951d6b21d67e1abf159e8c6f90f.pdf
Complexification
Lipschitz algebra
Lipschitz involution
Quasicompact operator
Riesz operator
Unital endomorphism
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-01-01
09
1
15
32
10.22130/scma.2018.22984
22984
مقاله پژوهشی
On an atomic decomposition in Banach spaces
Telman Gasymov
department2011@mail.ru
1
Chingiz Hashimov
chingiz.heshimov.88@mail.ru
2
Department of Non-harmonic analysis,Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
Ganja State University, Ganja, Azerbaijan.
An atomic decomposition is considered in Banach space. A method for constructing an atomic decomposition of Banach space, starting with atomic decomposition of subspaces is presented. Some relations between them are established. The proposed method is used in the study of the frame properties of systems of eigenfunctions and associated functions of discontinuous differential operators.
http://scma.maragheh.ac.ir/article_22984_651c11798bcd8c9dc55de818395c15bd.pdf
$p$-frames
$tilde{X}$-frames
Conjugate systems to $tilde{X}$
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-01-01
09
1
33
43
10.22130/scma.2018.23682
23682
مقاله پژوهشی
Density near zero
Elham Bayatmanesh
bayatmanesh.e@gmail.com
1
Mohammad Akbari Tootkaboni
tootkaboni.akbari@gmail.com
2
Department of Mathematics, Faculty of Basic Science, Shahed University, Tehran, Iran.
Department of Mathematics, Faculty of Basic Science, Shahed University, Tehran, Iran.
Let $S$ be a dense subsemigroup of $(0,+infty)$. In this paper, we state definition of thick near zero, and also we will introduce a definition that is equivalent to the definition of piecewise syndetic near zero which presented by Hindman and Leader in [6]. We define density near zero for subsets of $S$ by a collection of nonempty finite subsets of $S$ and we investigate the conditions under these concepts.
http://scma.maragheh.ac.ir/article_23682_545b6075235df500f5ed73aa31024524.pdf
The Stone-Cech compactification
Density
Piecewise syndetic set near zero
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-01-01
09
1
45
83
10.22130/scma.2018.24755
24755
مقاله پژوهشی
On the stability of the Pexiderized cubic functional equation in multi-normed spaces
Mahdi Nazarianpoor
mehdi.nazarianpoor@yahoo.com
1
Ghadir Sadeghi
ghadir54@gmail.com
2
Department of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.
Department of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.
In this paper, we investigate the Hyers-Ulam stability of the orthogonally cubic equation and Pexiderized cubic equation <br />[<br />f(kx+y)+f(kx-y)=g(x+y)+g(x-y)+frac{2}{k}g(kx)-2g(x),<br />]<br />in multi-normed spaces by the direct method and the fixed point method. Moreover, we prove the Hyers-Ulam stability of the $2$-variables cubic equation <br />[<br /> f(2x+y,2z+t)+f(2x-y,2z-t) =2f(x+y,z+t) +2f(x-y,z-t)+12f(x,z),<br />]<br />and orthogonally cubic type and $k$-cubic equation in multi-normed spaces. A counter example for non stability of the cubic equation is also discussed.
http://scma.maragheh.ac.ir/article_24755_41cdb890766a677f5346e922caa5ad31.pdf
Hyers-Ulam stability
Multi-normed space
Cubic functional equation
Pexiderized cubic functional equation
$2$-variables cubic functional equation
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-01-01
09
1
85
112
10.22130/scma.2018.24627
24627
مقاله پژوهشی
Non-Archimedean fuzzy metric spaces and Best proximity point theorems
Mohadeseh Paknazar
m.paknazar@yahoo.com
1
Department of Mathematics, Farhangian University, Iran.
In this paper, we introduce some new classes of proximal contraction mappings and establish best proximity point theorems for such kinds of mappings in a non-Archimedean fuzzy metric space. As consequences of these results, we deduce certain new best proximity and fixed point theorems in partially ordered non-Archimedean fuzzy metric spaces. Moreover, we present an example to illustrate the usability of the obtained results.
http://scma.maragheh.ac.ir/article_24627_22f14f4b196640de19b797939e8e6153.pdf
Fuzzy metric space
Best proximity point
Proximal contraction
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-01-01
09
1
113
128
10.22130/scma.2018.23645
23645
مقاله پژوهشی
On the cyclic Homology of multiplier Hopf algebras
Ghorbanali Haghighatdoost
gorbanali@azaruniv.ac.ir
1
Hami Abbasi Makrani
abbasi.makrani@gmail.com
2
Rasoul Mahjoubi
rasoolmahjoubi@yahoo.com
3
Department of Mathematics, Faculty of Science, Azarbaijan shahid Madani university, Tabriz, Iran.
Department of Mathematics, Faculty of Science, Azarbaijan shahid Madani university, Tabriz, Iran.
Department of Mathematics, Faculty of Science, Azarbaijan shahid Madani university, Tabriz, Iran.
In this paper, we will study the theory of cyclic homology for regular multiplier Hopf algebras. We associate a cyclic module to a triple $(mathcal{R},mathcal{H},mathcal{X})$ consisting of a regular multiplier Hopf algebra $mathcal{H}$, a left $mathcal{H}$-comodule algebra $mathcal{R}$, and a unital left $mathcal{H}$-module $mathcal{X}$ which is also a unital algebra. First, we construct a paracyclic module to a triple $(mathcal{R},mathcal{H},mathcal{X})$ and then prove the existence of a cyclic structure associated to this triple.
http://scma.maragheh.ac.ir/article_23645_980a6fd18602b47503b690dd49acad52.pdf
Multiplier Hopf algebra
Cyclic homology
Cyclic module
Paracyclic module
$H-$comodule
$H-$module
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-01-01
09
1
129
142
10.22130/scma.2018.23847
23847
مقاله پژوهشی
Frames in super Hilbert modules
Mehdi Rashidi-Kouchi
m_rashidi@kahnoojiau.ac.ir
1
Young Researchers and Elite Club Kahnooj Branch, Islamic Azad University, Kerman, Iran.
In this paper, we define super Hilbert module and investigate frames in this space. Super Hilbert modules are generalization of super Hilbert spaces in Hilbert C*-module setting. Also, we define frames in a super Hilbert module and characterize them by using of the concept of g-frames in a Hilbert C*-module. Finally, disjoint frames in Hilbert C*-modules are introduced and investigated.
http://scma.maragheh.ac.ir/article_23847_a719336ebb8e112974c326ddac5e743a.pdf
Super Hilbert
Frame
G-Frame
Hilbert $C^*$-module
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2018-01-01
09
1
143
150
10.22130/scma.2018.24756
24756
مقاله پژوهشی
A cone theoretic Krein-Milman theorem in semitopological cones
Ali Hassanzadeh
a_hassanzadeh@sut.ac.ir
1
Ildar Sadeqi
esadeqi@sut.ac.ir
2
Department of Mathematics, Sahand University of Technology, Tabriz, Iran.
Department of Mathematics, Sahand University of Technology, Tabriz, Iran.
In this paper, a Krein-Milman type theorem in $T_0$ semitopological cone is proved, in general. In fact, it is shown that in any locally convex $T_0$ semitopological cone, every convex compact saturated subset is the compact saturated convex hull of its extreme points, which improves the results of Larrecq.
http://scma.maragheh.ac.ir/article_24756_68b4ace761054de875c4f7f9863370f7.pdf
$T_0$ topology
Extreme Point
Krein-Milman type theorem