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

Maryam Aghakoochaki; Ali Rejali

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

Functional Analysis 2022-12-20 v1

Authors: Maryam Aghakoochaki , Ali Rejali

Abstract

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.

Keywords

vector-valued Banach algebras locally compact groups BSE-Banach algebras convolution measure algebras L1 spaces measure algebras

Cite

@article{arxiv.2212.09106,
  title  = {$L_{1}$- Properties of vector-valued Banach algebras},
  author = {Maryam Aghakoochaki and Ali Rejali},
  journal= {arXiv preprint arXiv:2212.09106},
  year   = {2022}
}

Comments

arXiv admin note: text overlap with arXiv:2212.06131

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

Abstract

Keywords

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