Ali Rejali

University of Isfahan · Department of Mathematics

مکارم اخلاق

مکارم اخلاق

مکارم اخلاق

A collection of poem in Islam

Banach algebras

Banach algebras

In this paper, X is a locally compact Hausdorff space and \({\cal A}\) is a Banach algebra. First, we study some basic features of C0(X, \({\cal A}\)) related to BSE concept, which are gotten from \({\cal A}\). In particular, we prove that if C0(X, \({\cal A}\)) has the BSE property then \({\cal A}\) has so. We also establish the converse of this r...

In this paper, X is a locally compact Hausdorff space and A is a Banach algebra. First, we study some basic features of C0(X, A) related to BSE concept, which are gotten from A. In particular, we prove that if C0(X, A) has the BSE property then A has so. We also establish the converse of this result, whenever X is discrete and A has the BSE−norm pr...

راهنمای حل مسائل ریاضی

دیوان رباعیات و دو بیتی های دکتر علی رجالی(قسمت دوم)

سیری منظوم در اصول و فروع دین دکتر علی رجالی A colection of poems in principles of religion

A colection of quatrains poems دیوان رباعیات و دو بیتی های پروفسور علی رجالی

سیری منظوم از زندگانی چهارده معصوم

The BSE-Properties of Lp-vector valued algebras

Algebric and topological properties of Banach algebras(IV)

دیوان اشعار نوای دل A colection of poems

برداشتهایی از معرفت نفس Perceptions of self-knowledge

In this paper, we introduce the notion of σ−ideally Connes amenable for dual Banach algebras and give some hereditary properties for this new notion. We also investigate σ−ideally Connes amenability of 1 (G, ω). We show that if ω is a diagonally bounded weight function on discrete group G and σ is isometrically isomorphism of 1 (G, ω), then 1 (G, ω...

خاطراتی از پروفسور علی رجالی

Let A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathcal {A}}$$\end{document} be a commutative semisimple Banach algebra, X be a locally compact Hausdorff topolo...

A class of commutative Banach algebras which satisfy a Bochner-Schoenberg-Eberlein-type inequality was introduced by Takahasi and Hatori. We generalize this property for the commutative Fréchet algebra (Ꮽ, p ℓ) ℓ∈‫ގ‬. Moreover, we verify and generalize some of the main results in the class of Banach algebras, for the Fréchet case. We prove that all...

1.1 THE ANALOGUE OF WEIGHTED GROUP ALGEBRA FOR SEMITOPOLOGICAL SEMIGROUPS 13 1.1.1 Definitions and Preliminary Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.1.2 Weighted Convolution Measure Algebra Ma(S,ω) . . . . . . . . . . . . . . . . . . . . . 18 1.2 REGULARITY AND AMENABILITY OF THE SECOND DUAL OF WEIGHTED GROU...

Banach algebras . . . . . . . . . . . . . . . . . . . . . 11 1.1 The Wiener amalgam spaces L π (p,q) (G) on IN-groups 11 1.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.1.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Content 1.1 BSE- property of tensor product Banach algebras 9 1.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.1.2 BSE- properties of Banach algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.1.3 BSE- properties of tensor product Banach algebra ....

Let (X, d) be a metric space and E be a unital commutative Banach algebra. In this paper, we prove that the regularity of unital commutative Banach algebra E is a necessary and sufficient condition for regularity of Lip d (X, E), where (X, d) is a compact metric space. Moreover, we show that the vector-valued Lipschitz algebra Lip d (X, E) is regul...

Let A be a semisimple commutative Banach algebra with identity of norm one and G be a locally compact abelian group. In this paper, we study the BSE-Property forL 1 (G,A) and show that L1(G,A) is a BSE algebra if and only if A is so.

Let $G$ and $H$ be locally compact groups. $BM(G, H)$ denoted the Banach algebra of bounded bilinear forms on $C_{0}(G)\times C_{0}(H)$.In this paper, the homological properties of Bimeasure algebras are investigated. It is found and approved that the Bimeasure algebras $BM(G, H)$ is amenable if and only if $G$ and $H$ are discrete. The correlation...

Let $G$ be a locally compact Abelian group, and $w: G\to (0, \infty)$ be a Borel measurable weighted function. In this paper, the algebraic and topological properties of group algebra are studied and assessed. We show that the weighted group algebra $L^{1}(G, w)$ is regular if and only if $w$ is a nonquasianalytic weight function. Also $L^{1}(G, w)...

Let G be a locally compact Abelian group, and w : G → (0, ∞) be a Borel measurable weighted function. In this paper, the algebraic and topological properties of group algebra are studied and assessed. We show that the weighted group algebra L 1 (G, w) is regular if and only if w is a nonquasianalytic weight function. Also L 1 (G, w) is Tauberian, f...

In this paper, we determine the character space of the vector-valued Lipschitz algebra Lipd(X, E), where (X, d) is any metric space and E is a certain unital semisimple commutative *-Banach algebra.

Let $A$ and $B$ be commutative semisimple Banach algebras. In this paper, the $BSE$ and $BED$- property of tensor Banach algebra $A{\otimes}_{\gamma} B$ with respect to the Banach algebras $A$ and $B$ are assesed. In particular, $BSE$ and $BED$- structure of vector-valued group algebra $L_{1}(G, A)$ and $C^{*}$- algebra $C_{0}(X, A)$ characterized.

Let A and B be commutative semisimple Banach algebras. In this paper, the BSE and BED-property of tensor Banach algebra A⊗ γ B with respect to the Banach algebras A and B are assesed. In particular, BSE and BED-structure of vector-valued group algebra L 1 (G, A) and C *-algebra C 0 (X, A) characterized.

Let $G$ be a locally compact group and $A$ be a commutative semisimple Banach algebra over the scalar field $\mathbb{C}$. The correlation between different types of $BSE$- Banach algebras $A$, and the Banach algebras $L^{1}(G, A)$ are assessed. It is found and approved that $M(G, A) = L^{1}(G, A)$ if and only if $G$ is discrete. Furthermore, some p...

Let G be a locally compact group and A be a commutative semisimple Banach algebra over the scalar field C. The correlation between different types of BSE-Banach algebras A, and the Banach algebras L 1 (G, A) are assessed. It is found and approved that M (G, A) = L 1 (G, A) if and only if G is discrete. Furthermore, some properties of vector-valued...

Let X be a locally compact Hausdorff space, and A be a commutative semisim-ple Banach algebra over the scalar field C. The correlation between different types of BSE-Banach algebras A, and the Banach algebra C 0 (X, A) are assessed. It is found and approved that C 0 (X, A) is a C *-algebra if and only if A is so. Furthermore, C b (X, A) = C 0 (X, A...

Let $X$ be a locally compact Hausdorff space, and $A$ be a commutative semisimple Banach algebra over the scalar field $\mathbb{C}$. The correlation between different types of BSE- Banach algebras $A$, and the Banach algebra $C_{0}(X, A)$ are assessed. It is found and approved that $C_{0}(X, A)$ is a $C^{*}$- algebra if and only if $A$ is so. Furth...

Let $\frak{F}(X, A)$ be one of the Banach algebras $\hbox{Lip}(X, A)$ or $\hbox{lip}(X, A)$. In this paper, we show that $\frak{F}(X, A)$ is amenable if and only if $X$ is uniformly discrete and $A$ is amenable. We also prove that the result holds for $\hbox{lip}^\circ(X, A)$ instead of $\frak{F}(X, A)$. In the case where $A^*$ is separable, we est...

In this paper, we investigate homological properties of Banach algebras. We show that retractions Banach algebras preserve biprojectivity, contractibility and biflatness. We also prove that contractibility of second dual of a Banach algebra implies contractibility of the Banach algebra. For a Banach algebra $A$ with $\Delta(A)\neq\emptyset$, let $\...

In this paper, we study the weak amenability of weighted measure algebras and prove that $M(G, \omega)$ is weakly amenable if and only if $G$ is discrete and every bounded quasi-additive function is inner. We also study the weak amenability of $L^1(G, \omega)^{**}$ and $M(G, \omega)^{**}$ and show that the weak amenability of theses Banach algebras...

In this paper, we deal with cohomological properties of weak amenability, cyclic amenability, cyclic weak amenability and point amenability of Banach algebras. We look at some hereditary properties of them and show that continuous homomorphisms with dense range preserve cyclically weak amenability, however, weak amenability and cyclically amenabili...

In this paper, we introduce and investigate the concepts of cyclically weakly amenable and point amenable. Then, we compare these concepts with the concepts of weakly amenable and cyclically amenable and find the relation between them. For example, we prove that a Banach algebra is weakly amenable if and only if it is both cyclically amenable and c...

In this paper, we study weak amenability of Beurling algebras. To this end, we introduce the notion inner quasi-additive functions and prove that for a locally compact group $G$, the Banach algebra $L^1(G, \omega)$ is weakly amenable if and only if every non-inner quasi-additive function in $L^\infty(G, 1/\omega)$ is unbounded. This provides an ans...

Experience and biography of Prof.Rejali

Let G be a generalized matrix Banach algebra associated with a Morita context \((A, B, M, N, \Phi , \Psi ).\) In this paper, we investigate biprojectivity and biflatness of G, under certain conditions. Indeed, we obtain a biprojective (resp. biflat) generalized matrix Banach algebra such that \(M\ne 0\) and \(N\ne 0.\) Moreover, we give a sufficien...

Let A be a commutative and semisimple Banach algebra with identity norm one and G be an abelian locally compact Hausdorff group. In this paper, we study BSE-Property for L 1 (G, A) and show that L 1 (G, A) is a BSE algebra if and only if A is so.

Let $ \mathcal{A} $ be a commutative and semisimple Banach algebra with identity norm one and $ G $ be an abelian locally compact Hausdorff group. In this paper, we study BSE-Property for $L^1(G,\mathcal A)$ and show that $L^1(G,\mathcal A)$ is a BSE algebra if and only if $\mathcal A$ is so.

List of graduate students

Let $\mathcal A$ be a separable Banach algebra, $G$ be a locally compact Hausdorff group and $1< p<\infty$. In this paper, we first provide a necessary and sufficient condition, for which $L^p(G,\mathcal A)$ is a Banach algebra, under convolution product. Then we characterize the character space of $L^p(G,\mathcal A)$, in the case where $\mathcal A...

خاطرات،زندگی نامه و تجارب پروفسور علی رجالی

درس هایی که در زندگی آموختم

دیوان قصاید چلچراغ

Rejali papers in weighted Banach algebras

Rejali papers in Banach algebras

Rejali papers in configurations

Rejali papers in Freshet algebras

Rejali papers in amenability

Rejali papers in regularity

Let $A$ be a commutative semisimple Arens regular unital Banach algebra. The correlation between the BSE-property of the Banach algebra $A$ and its second duals are assessed. It is found and approved that if $A$ is a BSE-algebra, then so is $A^{**}$. The opposite correlation will hold in certain conditions. The correlation of the BSE-norm property...

Let $A$ be a commutative semisimple Arens regular unital Banach algebra. The correlation between the BSE-property of the Banach algebra $A$ and its second duals are assessed. It is found and approved that if $A$ is a BSE-algebra, then so is $A^{**}$. The opposite correlation will hold in certain conditions. The correlation of the BSE-norm property...

In this paper, we introduce a new notion of amenability, $\sigma-$Connes ideal, say, for a large class of dual Banach algebras. We extend the concept of ideal Connes amenability and study their properties. Let $\sigma$ be a $weak^{*}$-continuous endomorphism on a dual Banach algebra $\mathcal{A}$ with dense range. Then the concept of ideal Connes-a...

In this paper, we study several type of point derivations for Banach algebras. We investigate how our definition of point derivations are related to each others.

In This paper, we study the concept of weakly almost periodic functions on Frechet algebras. For a Frechet algebra A, we show that WAP(A)=wap(A). We also show that A** is Arens regular if and only if both A and WAP(A)* are Arens regular. Finally, for a sequence of Frechet algebras (An), we prove that the Frechet algebra \ell^1-\prod An is Arens reg...

In this paper, we study several type of point derivations for Banach algebras. We investigate how our definition of point derivations are related to each others.

Let $A$ be a commutative semisimple Banach algebra, $X$ be a locally compact Hausdorff topological space and $G$ be a locally compact topological group. In this paper, we investigate several properties of vector valued Banach algebras $C_0(X,A)$, $L^p(G,A)$, $l^p(X,A)$ and $l^{\infty}(X,A)$. We prove that these algebras are isomorphic with a $C^*-$...

C.V.of Prof.Ali Rejali

Let ω be a weight function on a locally compact group G and let M * (G, ω) be the subspace of M (G, ω) * consisting of all functionals that vanish at infinity. In this paper, we first investigate the Arens regularity of M * (G, ω) * and show that M * (G, ω) * is Arens regular if and only if G is finite or Ω is zero cluster. This result is an answer...

Let $\omega $ be a weight function on a locally compact group G mand let $ M_* (G, \omega ) $ be the subspace of $ M(G , \omega )^* $ consisting of all functionals that vanish at infinity. In this paper, we first investigate the Arens regularity of $ M_* (G, \omega )^* $ and show that $ M_* (G, \omega )^* $ is Arnes regular if and only if G is fini...

در این کتاب مجموعه قصاید اینجاب امده است

Let (X, d) be a metric space and α > 0. In this paper, we study extensions of some complex-valued Lipschitz functions, from some special subset X 0 to X. These extensions are with no-increasing Lipschitz number or the smallest Lipschitz number. Moreover, we show that under some conditions, Tietze extension theorem can be generalized for Lipschitz f...

Let (X,d) be a metric space and $ \alpha > 0 $. In this paper, we study extensions of some complex-valued Lipschitz functions, from some special subset $ X_0 $ to X. These extensions are with no-increasing Lipschitz number or the smallest Lipschitz number. Moreover, we show that under some conditions, Tietze extension theorem can be generalized for...

Let (X, d) be a metric space with at least two elements and (A, p l) be a commutative semisimple Frechet algebra over the scalar field C. The correlation between the BSE-property of the Frechet algebra (A, p l) and Lip d (X, A) is assessed. It is found and approved that if Lip d (X, A) is a BSE-Frechet algebra, then so is A. The opposite correlatio...

Let $( X,d )$ be a metric space with at least two elements and $( A , p_l )$ be a commutative semisimple Frechet algebra over the scalar field of complex numbers. The correlation between the BSE-property of the Frechet algebra $( A , p_l )$ and $\Lip_{d}( X , A )$ is assessed. It is found and approved that if $\Lip_{d}( X , A )$ is a BSE-Frechet al...

The notion of Fréchet locally C *-algebra generalizes the notion of C *-algebra. In this paper, we first present some definitions and basic facts about locally C *-algebra, and then we introduce and study the notion of ideal a and weak menability for these algebras. Also,we show that every Fréchet locally C *-algebra is ideally amenable.

در این کتاب حکومت حضرت علی (ع) به صورت مثنوی سروده شده است

The notion of Fr\'{e}chet locally $C^*$-algebra generalizes the notion of $C^*$-algebra. In this paper, we first present some definitions and basic facts about locally $C^*$-algebra, and then we introduce and study the notion of ideal and weak amenability for these algebras. Also, we show that every Fr\'{e}chet locally $C^*$-algebra is ideally amen...

In this paper we study the notion of configuration for group actions. It is proved that some properties concerning configuration of groups can be extended for the case of group actions. The relationship between configuration and different types of well-known ping-pong lemma is also investigated.

In this paper we introduce and study some notations of amenability such as n-ideal amenability and n-weak amenability for Fréchet algebra and we examine how these concepts in Banach algebra can be generalized and defined for Fréchet algebra. We will also examine some inherited properties of n-ideal and n-weak amenable Fréchet algebra and determine...

In this paper, we introduce and study some notations of amenability such as $n$-ideal amenability and $n$-weak amenability for Frechet algebra and we examine how these concepts in Banach algebra can be generalized and defined for Frechet algebra. We will also examine some inherited properties of $n$-ideal and $n$-weak amenable Frechet algebra and d...

در این کتاب حکومت اسلامی در دوران حضرت علی به صورت نظم سروده شده است

In this paper we define countable-configuration of groups and prove that two Hopfian groups with the same set of countable-configurations are isomorphic and vice versa. We also study the count-able paradoxical decomposition of groups. It is proved that a group G admits a countable paradoxical decomposition if and only if it is infinite.

In this paper we define countable-configuration of groups and prove that two Hopfian groups with the same set of countable-configurations are isomorphic and vice versa. We also study the countable paradoxical decomposition of groups. It is proved that a group G admits a countable paradoxical decomposition if and only if it is infinite.

Let A and B be two Banach algebras and ?? ?(B): In this paper, we investigate biprojectivity and biflatness of ?-Lau product of Banach algebras A x? B. Indeed, we show that A x? B is biprojective if and only if A is contractible and B is biprojective. This generalizes some known results. Moreover, we characterize biflatness of ?-Lau product of Bana...

Let (X, d) be a metric space and A be a commutative Banach algebra such that ∆(A) be nonempty. In this paper, we provide necessary and sufficient conditions, under which C BSE (∆(A)) is a Dual Banach algebra. Moreover, we provide some conditions for that Lipα(X, A) is a Dual Banach algebra.

Let $ ( X , d ) $ be a metric space and $ A $ be a commutative Banach algebra such that $ \Delta ( A ) $ be nonempty. In this paper, we provide necessary and sufficient conditions, under which $ C_{BSE} ( \Delta (A) ) $ is a Dual Banach algebra. Moreover, we provide some conditions for that $ Lip_{\alpha} ( X , A ) $ is a Dual Banach algebra.

LI,3 Abstract. Let G be a locally compact group and 1 ≤ p < ∞. Based on some important earlier works, in this paper the concept of LT p −function is introduced. Then the structure of the space LT p (G), which is consisting of all LT p −functions, is investigated. As an important result, LT p (G)+ is completely characterized, for the class of amenab...

Let $G$ be a locally compact group and $1\leq p<\infty$. Based on some important earlier works, in this paper the concept of $L_p^T-$function is introduced. Then the structure of the space $L^{T}_p(G)$, which is consisting of all $L_p^T-$functions, is investigated. As an important result, $L^{T}_p(G)^+$ is completely characterized, for the class of...