English

Factorization and weak amenability of A(X)

Functional Analysis 2007-05-23 v1 Operator Algebras

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).

Keywords

Cite

@article{arxiv.math/0311525,
  title  = {Factorization and weak amenability of A(X)},
  author = {Niels Grønbæk},
  journal= {arXiv preprint arXiv:math/0311525},
  year   = {2007}
}

Comments

19 pages, submitted