Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

A characterization for contractible Banach algebras

Document Type : Original Paper

Authors
Maysam Maysami Sadr
Jamal Rooin
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
Banach algebra
amenability
contractibility
category of Banach modules
Subjects
 B.E. Johnson, Cohomology in Banach algebras, Memoirs of the American Mathematical Society, vol. 127, 1972.
 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.

  • Receive Date 02 November 2022
  • Revise Date 28 June 2023
  • Accept Date 01 July 2023