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Ali Ebadian

Publications and source records attributed to Ali Ebadian.

14 recordsLinked to original sources
arXiv2022

Some Results on Matricial Field C-Algebras

In this paper, we consider Blackadar and Kirchberg's MF algebras. We show that any inner quasidiagonal C-algebra is MF algebra and we generalize Voiculescu's Representation Theorem for a special version of MF algebras. Moreover, we define a weak version of MF algebras namely matrical amenable (AM) algebras, and prove some results related to this new notion. Finally, we consider real C-algebras and we show that a real C-algebra is MF if and only if its complexification is MF.

math.OA↗
arXiv2020

Characterization of Symmetric Amenability of Unital Banach Algebras

In this paper, we introduce $p$-amenability, bounded $s$-symmetric approximate and $s$-symmetric virtual diagonals for a Banach algebra $\mathfrak{A}$ where $s$ is a non-zero element of algebraic center of $\mathfrak{A}$ that is denoted by $Z(\mathfrak{A})$. We show that if a Banach algebra $\mathfrak{A}$ is $p$-amenable then it has bounded $s$-symmetric approximate and $s$-symmetric virtual diagonals and by this fact we prove that if the Banach algebra $\mathfrak{A}$ is unital then $p$-amenability and symmetric amenability are equivalent.

math.FA↗
arXiv2020

Amenability and Inner Amenability of Transformation Groups

In this paper, we show that there is a net for amenable transformation groups like F{\o}lner net for amenable groups and investigate amenability of a transformation group constructed by semidirect product of groups. We introduce inner amenability of transformation groups and characterize this property.

math.FA↗
arXiv2020

Quasi-isometric embedding between $*$-algebras

The concept of quasi-isometric embedding maps between $*$-algebras is introduced. We have obtained some basic results related to this notion and similar to quasi-isometric embedding maps on metric spaces, under some conditions, we give a necessary and sufficient condition on a $*$-homomorphism to be a quasi-isometric embedding between $*$-algebras.

math.FA↗
arXiv2020

A Weak Form of Amenability of Topological Semigroups and its Applications in Ergodic and Fixed Point Theories

In this paper, we introduce a weak form of amenability on topological semigroups that we call $φ$-amenability, where $φ$ is a character on a topological semigroup. Some basic properties of this new notion are obtained and by giving some examples, we show that this definition is weaker than the amenability of semigroups. As a noticeable result, for a topological semigroup $S$, it is shown that if $S$ is $φ$-amenable, then $S$ is amenable. Moreover, $φ$-ergodicity for a topological semigroup $S$ is introduced and it is proved that under some conditions on $S$ and a Banach space $X$, $φ$-amenability and $φ$-ergodicity of any antirepresntation defined by a right action $S$ on $X$, are equivalent. A relation between $φ$-amenability of topological semigroups and existance of a common fixed point is investigated and by this relation, Hahn-Banach property of topological semigroups in the sense of $φ$-amenability defined and studied.

math.FA↗
arXiv2019

Some properties of bounded tri-linear maps

Let $X,Y,Z$ and $W$ be normed spaces and $f:X\times Y\times Z\longrightarrow W $ be a bounded tri-linear mapping. In this Article, we define the topological centers for bounded tri-linear mapping and we invistagate thier properties. We study the relationships between weakly compactenss of bounded linear mappings and regularity of bounded tri-linear mappings. For both bounded tri-linear mappings $f$ and $g$, let $f$ factors through $g$, we present necessary and suficient condition such that the extensions of $f$ factors through extensions of $g$. Also we establish relations between regularity and factorization property of bounded tri-linear mappings.

math.FA↗
arXiv2019

Regularity of bounded tri-linear maps and the fourth adjiont of a tri-derivation

In this Article, we give a simple criterion for the regularity of a tri-linear mapping. We provide if $f:X\times Y\times Z\longrightarrow W $ is a bounded tri-linear mapping and $h:W\longrightarrow S$ is a bounded linear mapping, then $f$ is regular if and only if $hof$ is regular. We also shall give some necessary and sufficient conditions such that the fourth adjoint $D^{****}$ of a tri-derivation $D$ is again tri-derivation.

math.FA↗
arXiv2019

Close-to-regularity and completely regularity of bounded tri-linear maps

Let $f:X\times Y\times Z\longrightarrow W $ be a bounded tri-linear map on normed spaces. We say that $f$ is close-to-regular when $f^{t****s}=f^{s****t}$ and we say that $f$ is completely regular when all natural extensions are equal. In this manuscript, we have some results on the close-to-regular maps and investigate the close-to-regularity of tri-linear maps. We investigate the relation between Arens regularity of bounded bilinear maps and close-to-regularity bounded tri-linear maps. We give a simple criterion for the completely regularity of tri-linear maps. We provide a necessary and sufficient condition such that the fourth adjoint $D^{****}$ of a tri-derivation is again a tri-derivation.

math.FA↗
arXiv2019

Calculating max-eigenvalues and max-eigenvectors with jumps of matrices

The eigenvalue problem for an irreducible non negative matrix $A=[a_{ij}]$ in the max-algebra is the form $A \otimes x = λx$ where $(A \otimes x)_i = \max (a_{ij}x_j), x=(x_1,x_2, \dots, x_n)^t $ and $λ$ refers to maximum cycle geometric mean $μ(A) $. In this paper we exhibit a method to compute $μ(A)$ and max-eigenvector by using mutation of matrices. Since the order of power method algorithm is $O(n^3)$, the advantage of this paper present a faster procedure.

math.FA↗
arXiv2016

Relative reproducing kernels in vector-valued Hilbert and Banach spaces

This paper is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular we extend reproducing kernels to relative reproducing kernels and prove some theorems in this subject.

math.FA↗