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Mohammad Fozouni

Publications and source records attributed to Mohammad Fozouni.

10 recordsLinked to original sources
arXiv2018

On two refinements of the bounded weak approximate identities

Let $A$ be a commutative Banach algebra with non-empty character space $Δ(A)$. In this paper, we change the concepts of convergence and boundedness in the classical notion of bounded approximate identity. This work give us a new kind of approximate identity between bounded approximate identity and bounded weak approximate identity. More precisely, a net $\{e_α\}$ in $A$ is a \emph{c-w approximate identity} if for each $a\in A$, the Gel'fand transform of $e_αa$ tends to the Gel'fand transform of $a$ in the compact-open topology and we say $\{e_α\}$ is \emph{weakly bounded} if the image of $\{e_α\}$ under the Gel'fand transform is bounded in $C_{0}(Δ(A))$.

math.FA↗
arXiv2018

BSE-property for some certain Segal and Banach algebras

For a commutative semi-simple Banach algebra ${A}$ which is an ideal in its second dual we give a necessary and sufficient condition for an essential abstract Segal algebra in ${A}$ to be a BSE-algebra. We show that a large class of abstract Segal algebras in the Fourier algebra $A(G)$ of a locally compact group $G$ are BSE-algebra if and only if they have bounded weak approximate identities. Also, in the case that $G$ is discrete we show that $A_{\rm cb}(G)$ is a BSE-algebra if and only if $G$ is weakly amenable. We study the BSE-property of some certain Segal algebras implemented by local functions that were recently introduced by J. Inoue and S.-E. Takahasi. Finally we give a similar construction for the group algebra implemented by a measurable and sub-multiplicative function.

math.FA↗
arXiv2018

On a question related to bounded approximate identities of ideals in Banach algebras

In this paper we give an example of a Banach algebra $A$ and a closed ideal $I$ of $A$ such that the multiplier algebra of $I$ is equal to $A$ but $I$ does not have any bounded approximate identity. In the case that $I$ has an approximate identity, we give a necessary condition on $I$ for which $A=\mathcal{M}(I)$, where $\mathcal{M}(I)$ denotes the multiplier algebra of $I$. Finally, as a corollary of our results, we show that the Fourier algebra of an amenable group is strictly dense in the Fourier-Stieltjes algebra.

math.FA↗
arXiv2017

On character space of the algebra of BSE-functions

Suppose that $A$ is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra $C_{\rm{BSE}}(Δ(A))$ consisting of all BSE-functions on $Δ(A)$ where $Δ(A)$ denotes the character space of $A$. Indeed, in the case that $A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a complete characterization of $Δ(C_{\rm{BSE}}(Δ(A)))$ and in the general case we give a partial answer. Also, using the Fourier algebra, we show that $C_{\rm{BSE}}(Δ(A))$ is not a $C^*$-algebra in general. Finally for some subsets $E$ of $A^*$, we define the subspace of BSE-like functions on $Δ(A)\cup E$ and give a nice application of this space related to Goldstine's theorem.

math.FA↗
arXiv2016

N-multipliers and their relations with n-homomorphisms

Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule. We introduce and study the notions of $n$-multipliers and approximate local $n$-multipliers by generalizing the classical concept of multipliers from $A$ into $X$. As an algebraic result, we construct a Banach algebra consisting of $n$-multipliers on $A$ and under some mild conditions, we give a nice relation of this algebra with $n$-homomorphisms from $A$ into $\mathbb{C}$.

math.FA↗
arXiv2015

Generalized injectivity of Banach modules

In this paper, we study the notion of $ϕ$-injectivity in the special case that $ϕ=0$. For an arbitrary locally compact group $G$, we characterize the 0-injectivity of $L^{1}(G)$ as a left $L^{1}(G)$ module. Also, we show that $L^{1}(G)^{**}$ and $L^{p}(G)$ for $1<p<\infty$ are 0-injective Banach $L^{1}(G)$ modules.

math.FA↗
arXiv2014

On $Δ$-weak $ϕ$-amenability of Banach algebras

Let $A$ be a Banach algebra and $ϕ\in Δ(A)\cup\{0\}$. We say that $A$ is $Δ$-weak $ϕ$-amenable if there exists an $m\in A^{**}$ such that $m(ϕ)=0$ and $m(ψ.a)=ψ(a)$ for each $ψ\in Δ(A)$ and $a\in \ker(ϕ)$. It is shown that $A$ is $Δ$-weak $ϕ$-amenable if and only if $\ker(ϕ)$ has a bounded $Δ$-weak approximate identity. We examine this notion for some algebras over amenable locally compact groups. Also we prove that every $Δ$-weak $ϕ$-amenable Banach algebra has a bounded $Δ$-weak approximate identity.

math.FA↗
arXiv2014

Amenable groups and bounded $Δ$-weak approximate identities

Let $A$ be a Banach algebra with a non-empty character space. We say that a bounded net $\{e_α\}$ in $A$ is a bounded $Δ$-weak approximate identity for $A$ if, for each $a\in A$ and compact subset $K$ of $Δ(A)$, $||\widehat{e_αa}-\widehat{a}||_{K}=\sup_{ϕ\in K}|ϕ(e_αa)-ϕ(a)|\rightarrow 0$. For each $1<p<\infty$, we prove that the Figa-Talamanca Herz algebra, $A_{p}(G)$ has a bounded $Δ$-weak approximate identity if and only if $G$ is an amenable group. Also we give a sufficient condition for amenability of group $G$.

math.FA↗