Self-induced Banach algebras

2003/11/28 by Niels Grønbæk, Grønbæk, Niels
Mathematics · #16D90 (Secondary) #46M18 #47L10 (Primary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:16D90 #msc:46M18 #msc:47L10

paper · pdf · doi:10.48550/arxiv.math/0311528

14 pages, submitted to conference proceedings

arxiv created 2003/11/28 · openalex publication_date 2003/11/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Banach algebra A is self-induced if the multiplication is an isomorphism from the A-balanced projective tensor-square of A to A. The class of self-induced Banach algebras is a natural generalization of unital Banach algebras, providing a fertile framework for developing homological aspects of unital Banach algebras. Elementary results with applictions to computations of the bounded Hochschild cohomology groups H¹(A,A^*) with emphasis on A=A(X), the approximable operators on a Banach space X, are given.

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