A characterization for contractible Banach algebras

Maysami Sadr, Maysam; Rooin, Jamal

doi:10.22055/jamm.2023.42251.2110

A characterization for contractible Banach algebras

Document Type : Original Paper

Authors

Department of Mathematics, Institute for Advanced Studies in Basic Sciences, Zanjan, Iran

10.22055/jamm.2023.42251.2110

Abstract

In this short note, the following new characterization of contractibility is stated and proved: A Banach algebra is contractible if and only if for any pair of Banach bimodules over that algebra, the closed linear subspace of all continuous bimodule morphisms between them, in the space of all bounded linear operators between them, is naturally topological complemented. Here, the phrase ``natural'' has been used with its meaning in Category Theory.

Keywords

Main Subjects

Functional Analysis

References

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O.T. Mewomo, Various notions of amenability in Banach algebras, Expositiones Mathematicae 29 (2011) 283–299.
V. Runde, Lectures on amenability, Springer-Verlag, Berlin, Heidelberg, 2002.
V. Runde, Amenable Banach algebras, Springer Monographs in Mathematics, Berlin, 2020.