Research ArticleNo Access

Banach valued algebras defined by a family of Banach algebras

Ali Ebadian

Department of Mathematics, Urmia University, Urmia, Iran

E-mail Address: ebadian.ali@gmail.com

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Madjid Eshaghi Gordji

Faculty of Science, Department of Mathematics, Semnan University, Semnan, Iran

E-mail Address: meshaghi@semnan.ac.ir

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, and

Ali Jabbari

Department of Mathematics, Urmia University, Urmia, Iran

E-mail Address: jabbari_al@yahoo.com

Corresponding author.

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https://doi.org/10.1142/S0219498824502062Cited by:0 (Source: Crossref)

Abstract

Let $Λ$ $Λ$ be a direct set, ${A_{α}}_{α \in Λ}$ ${A_{α}}_{α \in Λ}$ be a family of Banach algebras with bounded approximate identity (or unital) and $I$ $I$ be a set. We consider the Banach algebra $ℓ^{\infty} (ℓ_{A_{β}} (I, A_{α}))$ $ℓ^{\infty} (ℓ_{A_{β}} (I, A_{α}))$ . We show that this algebra has a bounded approximate identity (or is unital) if and only if $I$ $I$ is finite. We also characterize the left multipliers of these algebras and investigate their amenability of them. Moreover, we characterize the character spaces (Gelfand spaces) of these algebras in a special case.

Communicated by Sergio Roberto López-Permouth

Keywords:

AMSC: 46H05, 43A20

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