Factorization and weak amenability of A(X)

Details Factorization and weak amenability of A(X) Factorization and weak amenability of A(X)

2003-11-28

arxiv.org/abs/math/0311525v1

Mathematics

Functional Analysis

19 pages, submitted

Scientific paper

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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