2021-10-21T00:18:39Z
https://scma.maragheh.ac.ir/?_action=export&rf=summon&issue=4776
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2018
09
1
Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions
Maliheh
Mayghani
Davood
Alimohammadi
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
2018
01
01
1
14
https://scma.maragheh.ac.ir/article_24240_91e55951d6b21d67e1abf159e8c6f90f.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2018
09
1
On an atomic decomposition in Banach spaces
Telman
Gasymov
Chingiz
Hashimov
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 $tilde{X}$
2018
01
01
15
32
https://scma.maragheh.ac.ir/article_22984_651c11798bcd8c9dc55de818395c15bd.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2018
09
1
Density near zero
Elham
Bayatmanesh
Mohammad
Akbari Tootkaboni
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
2018
01
01
33
43
https://scma.maragheh.ac.ir/article_23682_545b6075235df500f5ed73aa31024524.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2018
09
1
On the stability of the Pexiderized cubic functional equation in multi-normed spaces
Mahdi
Nazarianpoor
Ghadir
Sadeghi
In this paper, we investigate the Hyers-Ulam stability of the orthogonally cubic equation and Pexiderized cubic equation \[f(kx+y)+f(kx-y)=g(x+y)+g(x-y)+\frac{2}{k}g(kx)-2g(x),\]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 \[ f(2x+y,2z+t)+f(2x-y,2z-t) =2f(x+y,z+t) +2f(x-y,z-t)+12f(x,z),\]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
2018
01
01
45
83
https://scma.maragheh.ac.ir/article_24755_41cdb890766a677f5346e922caa5ad31.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2018
09
1
Non-Archimedean fuzzy metric spaces and Best proximity point theorems
Mohadeseh
Paknazar
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
2018
01
01
85
112
https://scma.maragheh.ac.ir/article_24627_22f14f4b196640de19b797939e8e6153.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2018
09
1
On the cyclic Homology of multiplier Hopf algebras
Ghorbanali
Haghighatdoost
Hami
Abbasi Makrani
Rasoul
Mahjoubi
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
2018
01
01
113
128
https://scma.maragheh.ac.ir/article_23645_980a6fd18602b47503b690dd49acad52.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2018
09
1
Frames in super Hilbert modules
Mehdi
Rashidi-Kouchi
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
2018
01
01
129
142
https://scma.maragheh.ac.ir/article_23847_a719336ebb8e112974c326ddac5e743a.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2018
09
1
A cone theoretic Krein-Milman theorem in semitopological cones
Ali
Hassanzadeh
Ildar
Sadeqi
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
2018
01
01
143
150
https://scma.maragheh.ac.ir/article_24756_68b4ace761054de875c4f7f9863370f7.pdf