On Pseudo-contractibility and Ultra Central Approximate Identity of Some Semigroup Algebras

Amir Sahami, Seyedeh Fatemeh Shariati and Xuanlong Ma

Journal of Mathematics, 2022, vol. 2022, 1-5

Abstract: In this paper, we investigate the existence of an ultra central approximate identity for a Banach algebra A and its second dual A∗∗. Also, we prove that for a left cancellative regular semigroup S, ℓ1S∗∗ has an ultra central approximate identity if and only if S is a group. As an application, we show that for a left cancellative semigroup S, ℓ1S∗∗ is pseudo-contractible if and only if S is a finite group. We also study this property for φ-Lau product Banach algebras and the module extension Banach algebras.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9527678

DOI: 10.1155/2022/9527678

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