Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions
Maliheh
Mayghani
Department of Mathematics, Payame Noor University, P. O. Box: 19359-3697, Tehran, Iran.
author
Davood
Alimohammadi
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran.
author
text
article
2018
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
09
v.
1
no.
2018
1
14
https://scma.maragheh.ac.ir/article_24240_91e55951d6b21d67e1abf159e8c6f90f.pdf
dx.doi.org/10.22130/scma.2018.24240
On an atomic decomposition in Banach spaces
Telman
Gasymov
Department of Non-harmonic analysis,Institute of Mathematics and
Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
author
Chingiz
Hashimov
Ganja State University, Ganja, Azerbaijan.
author
text
article
2018
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
09
v.
1
no.
2018
15
32
https://scma.maragheh.ac.ir/article_22984_651c11798bcd8c9dc55de818395c15bd.pdf
dx.doi.org/10.22130/scma.2018.22984
Density near zero
Elham
Bayatmanesh
Department of Mathematics, Faculty of Basic Science, Shahed University, Tehran, Iran.
author
Mohammad
Akbari Tootkaboni
Department of Mathematics, Faculty of Basic Science, Shahed University, Tehran, Iran.
author
text
article
2018
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
09
v.
1
no.
2018
33
43
https://scma.maragheh.ac.ir/article_23682_545b6075235df500f5ed73aa31024524.pdf
dx.doi.org/10.22130/scma.2018.23682
On the stability of the Pexiderized cubic functional equation in multi-normed spaces
Mahdi
Nazarianpoor
Department of Mathematics and Computer
Sciences, Hakim Sabzevari University, Sabzevar, Iran.
author
Ghadir
Sadeghi
Department of Mathematics and Computer
Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.
author
text
article
2018
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
09
v.
1
no.
2018
45
83
https://scma.maragheh.ac.ir/article_24755_41cdb890766a677f5346e922caa5ad31.pdf
dx.doi.org/10.22130/scma.2018.24755
Non-Archimedean fuzzy metric spaces and Best proximity point theorems
Mohadeseh
Paknazar
Department of Mathematics, Farhangian University, Iran.
author
text
article
2018
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
09
v.
1
no.
2018
85
112
https://scma.maragheh.ac.ir/article_24627_22f14f4b196640de19b797939e8e6153.pdf
dx.doi.org/10.22130/scma.2018.24627
On the cyclic Homology of multiplier Hopf algebras
Ghorbanali
Haghighatdoost
Department of Mathematics, Faculty of Science, Azarbaijan shahid Madani university, Tabriz, Iran.
author
Hami
Abbasi Makrani
Department of Mathematics, Faculty of Science, Azarbaijan shahid Madani university, Tabriz, Iran.
author
Rasoul
Mahjoubi
Department of Mathematics, Faculty of Science, Azarbaijan shahid Madani university, Tabriz, Iran.
author
text
article
2018
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
09
v.
1
no.
2018
113
128
https://scma.maragheh.ac.ir/article_23645_980a6fd18602b47503b690dd49acad52.pdf
dx.doi.org/10.22130/scma.2018.23645
Frames in super Hilbert modules
Mehdi
Rashidi-Kouchi
Young Researchers and Elite Club
Kahnooj Branch, Islamic Azad University, Kerman, Iran.
author
text
article
2018
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
09
v.
1
no.
2018
129
142
https://scma.maragheh.ac.ir/article_23847_a719336ebb8e112974c326ddac5e743a.pdf
dx.doi.org/10.22130/scma.2018.23847
A cone theoretic Krein-Milman theorem in semitopological cones
Ali
Hassanzadeh
Department of Mathematics, Sahand University of Technology, Tabriz, Iran.
author
Ildar
Sadeqi
Department of Mathematics, Sahand University of Technology, Tabriz, Iran.
author
text
article
2018
eng
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.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
09
v.
1
no.
2018
143
150
https://scma.maragheh.ac.ir/article_24756_68b4ace761054de875c4f7f9863370f7.pdf
dx.doi.org/10.22130/scma.2018.24756