arXiv subjects

Maryam Aghakoochaki

Publications and source records attributed to Maryam Aghakoochaki.

4 recordsLinked to original sources

arXiv2022

$L_{1}$- Properties of vector-valued Banach algebras

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 properties of vector-valued measure algebras on groups are given, so that $M(G, A)$ is a convolution measure algebra.

math.FA↗

arXiv2022

$C^{*}$- properties of vector-valued Banach algebras

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. Furthermore, $C_{b}(X, A)= C_{0}(X, A)$ if and only if $X$ is compact.

math.FA↗

arXiv2022

BSE-Properties of Second Dual of Banach Algebras

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 of the Banach algebra and its second dual are assessed and examined. It is revealed that, if $A$ is a commutative Arens regular unital Banach algebra where $A^{**}$ is semisimple, then, $A$ and $A^{**}$ are BSE-norm algebra.

math.FA↗

arXiv2021

The BSE property for vector-valued Frechet Lipschitz algebras

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 algebra, then so is $A$. The opposite correlation will hold if $( A , p_l )$ is unital.

math.FA↗