Cohomology of Banach algebras of operators and geometry of Banach spaces.

Research output: Contribution to journalArticle

Abstract

In the paper we give an exposition of the major results concerning the relation between first order cohomology of Banach algebras of operators on a Banach space with coefficients in specified modules and the geometry of the underlying Banach space. In particular we shall compare the properties weak amenability and amenability for Banach algebras A(X), the approximable operators on a Banach space X. Whereas amenability is a local property of the Banach space X, weak amenability is often the consequence of properties of large scale geometry.
Original languageEnglish
Pages (from-to)57-80
Number of pages24
JournalContemporary Mathematics
Volume435
Publication statusPublished - 2007

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