On pseudo-contractibility of certain algebras related to a discrete semigroup

Document Type : Research Paper

Authors

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

2 Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran.

3 Department of Basic Science, Babol Noshirvani University of Technology, Shariati Avenue, Babol 47148-71167, Iran.

10.29252/as.2021.2050

Abstract

In this paper, we introduce a notion of ultra central approximate identity for Banach algebras which is a generalization of the bounded approximate identity and the central approximate identity. Using this concept we study pseudo-contractibility of some matrix algebras among $\ell^1$-Munn algebras. As an application, for the Brandt semigroup $S=M^{0}(G,I)$ over a non-empty set $I$, we show that $\ell^{1}(S)$ has an ultra central approximate identity if and only if $I$ is finite. Also we show that the notion of pseudo-contractibility and contractibility are the same on $\ell^{1}(S)^{**}$, where $S$ is the Brandt semigroup.

Keywords


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