University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
09
1
2018
01
01
Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions
1
14
EN
Maliheh
Mayghani
Department of Mathematics, Payame Noor University, P. O. Box: 19359-3697, Tehran, Iran.
m_maighany@yahoo.com
Davood
Alimohammadi
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran.
alimohammadi.davood@gmail.com
10.22130/scma.2018.24240
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.
Complexification,Lipschitz algebra,Lipschitz involution,Quasicompact operator,Riesz operator,Unital endomorphism
https://scma.maragheh.ac.ir/article_24240.html
https://scma.maragheh.ac.ir/article_24240_91e55951d6b21d67e1abf159e8c6f90f.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
09
1
2018
01
01
On an atomic decomposition in Banach spaces
15
32
EN
Telman
Gasymov
Department of Non-harmonic analysis,Institute of Mathematics and
Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
department2011@mail.ru
Chingiz
Hashimov
Ganja State University, Ganja, Azerbaijan.
chingiz.heshimov.88@mail.ru
10.22130/scma.2018.22984
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.
$p$-frames,$tilde{X}$-frames,Conjugate systems to $tilde{X}$
https://scma.maragheh.ac.ir/article_22984.html
https://scma.maragheh.ac.ir/article_22984_651c11798bcd8c9dc55de818395c15bd.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
09
1
2018
01
01
Density near zero
33
43
EN
Elham
Bayatmanesh
Department of Mathematics, Faculty of Basic Science, Shahed University, Tehran, Iran.
bayatmanesh.e@gmail.com
Mohammad
Akbari Tootkaboni
Department of Mathematics, Faculty of Basic Science, Shahed University, Tehran, Iran.
tootkaboni.akbari@gmail.com
10.22130/scma.2018.23682
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.
The Stone-Cech compactification,Density,Piecewise syndetic set near zero
https://scma.maragheh.ac.ir/article_23682.html
https://scma.maragheh.ac.ir/article_23682_545b6075235df500f5ed73aa31024524.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
09
1
2018
01
01
On the stability of the Pexiderized cubic functional equation in multi-normed spaces
45
83
EN
Mahdi
Nazarianpoor
Department of Mathematics and Computer
Sciences, Hakim Sabzevari University, Sabzevar, Iran.
mehdi.nazarianpoor@yahoo.com
Ghadir
Sadeghi
Department of Mathematics and Computer
Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.
ghadir54@gmail.com
10.22130/scma.2018.24755
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.
Hyers-Ulam stability,Multi-normed space,Cubic functional equation,Pexiderized cubic functional equation,$2$-variables cubic functional equation
https://scma.maragheh.ac.ir/article_24755.html
https://scma.maragheh.ac.ir/article_24755_41cdb890766a677f5346e922caa5ad31.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
09
1
2018
01
01
Non-Archimedean fuzzy metric spaces and Best proximity point theorems
85
112
EN
Mohadeseh
Paknazar
0000-0001-9327-7911
Department of Mathematics, Farhangian University, Iran.
m.paknazar@yahoo.com
10.22130/scma.2018.24627
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.
Fuzzy metric space,Best proximity point,Proximal contraction
https://scma.maragheh.ac.ir/article_24627.html
https://scma.maragheh.ac.ir/article_24627_22f14f4b196640de19b797939e8e6153.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
09
1
2018
01
01
On the cyclic Homology of multiplier Hopf algebras
113
128
EN
Ghorbanali
Haghighatdoost
Department of Mathematics, Faculty of Science, Azarbaijan shahid Madani university, Tabriz, Iran.
gorbanali@yahoo.com
Hami
Abbasi Makrani
Department of Mathematics, Faculty of Science, Azarbaijan shahid Madani university, Tabriz, Iran.
abbasi.makrani@gmail.com
Rasoul
Mahjoubi
Department of Mathematics, Faculty of Science, Azarbaijan shahid Madani university, Tabriz, Iran.
rasoolmahjoubi@yahoo.com
10.22130/scma.2018.23645
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.
Multiplier Hopf algebra,Cyclic homology,Cyclic module,Paracyclic module,$H-$comodule,$H-$module
https://scma.maragheh.ac.ir/article_23645.html
https://scma.maragheh.ac.ir/article_23645_980a6fd18602b47503b690dd49acad52.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
09
1
2018
01
01
Frames in super Hilbert modules
129
142
EN
Mehdi
Rashidi-Kouchi
Young Researchers and Elite Club
Kahnooj Branch, Islamic Azad University, Kerman, Iran.
m_rashidi@kahnoojiau.ac.ir
10.22130/scma.2018.23847
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.
Super Hilbert,Frame,G-Frame,Hilbert $C^*$-module
https://scma.maragheh.ac.ir/article_23847.html
https://scma.maragheh.ac.ir/article_23847_a719336ebb8e112974c326ddac5e743a.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
09
1
2018
01
01
A cone theoretic Krein-Milman theorem in semitopological cones
143
150
EN
Ali
Hassanzadeh
Department of Mathematics, Sahand University of Technology, Tabriz, Iran.
a_hassanzadeh@sut.ac.ir
Ildar
Sadeqi
Department of Mathematics, Sahand University of Technology, Tabriz, Iran.
esadeqi@sut.ac.ir
10.22130/scma.2018.24756
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.
$T_0$ topology,Extreme Point,Krein-Milman type theorem
https://scma.maragheh.ac.ir/article_24756.html
https://scma.maragheh.ac.ir/article_24756_68b4ace761054de875c4f7f9863370f7.pdf