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Factorization and weak amenability of A(X)

2003/11/28 by Niels Grønbæk, Grønbæk, Niels
Mathematics · #16D90 (Secondary) #46M20 #47L10 (Primary) #Advanced Banach Space Theory #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:46M20 #msc:47L10

paper · pdf · doi:10.48550/arxiv.math/0311525

19 pages, submitted

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

We investigate weak amenability of the Banach algebra A(X) of approximable operators on a Banach space X and its relation to factorization properties of operators in A(X). We show that if A(X) is weakly amenable, then either A(X) is self-induced (a nice factorization property), or X is very special, combining some of the exotic properties of the spaces of Gowers and Maurey and of Pisier. In the class of self-induced Banach algebras we show that weak amenability is preserved under an equivalence of Morita type. Using this we extend some results of A. Blanco about weak amenability of A(X).

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