Research ArticleNo Access

On strong pseudo-amenability of some Banach algebras

Department of Mathematics, Faculty of Basic Sciences, Ilam University, P.O. Box 69315-516, Ilam, Iran

https://doi.org/10.1142/S1793557122500188Cited by:2 (Source: Crossref)

Abstract

In this paper, we introduce a new notion of strong pseudo-amenability for Banach algebras. We study strong pseudo-amenability of some matrix algebras. Using this tool, we characterize strong pseudo-amenability of $ℓ^{1} (S)$ , provided that $S$ is a uniformly locally finite inverse semigroup. As an application, we show that for a Brandt semigroup $S = M^{0} (G, I)$ , $ℓ^{1} (S)$ is strong pseudo-amenable if and only if $G$ is amenable and $I$ is finite. We give some examples to show the differences between strong pseudo-amenability and the other classical notions of amenability.

Communicated by N. C. Wong

Keywords:

AMSC: 46H05, 46M10, 20M18, 43A20

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