Amenability of algebras of approximable operators

Details Amenability of algebras of approximable operators Amenability of algebras of approximable operators

2008-04-10

arxiv.org/abs/0804.1725v1

Mathematics

Functional Analysis

20 pages, to appear in Israel Journal of Mathematics

Scientific paper

We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators, strengthening known results and developing new techniques to determine whether or not a given Banach space carries an amenable algebra of approximable operators. Using these techniques, we are able to show, among other things, the non-amenability of the algebra of approximable operators on Tsirelson's space.

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