A remark on contractible Banach algebras

Details A remark on contractible Banach algebras A remark on contractible Banach algebras

2011-10-27

arxiv.org/abs/1110.6216v1

Mathematics

Functional Analysis

3 pages

Scientific paper

It is a longstanding problem whether every contractible Banach algebra is
necessarily finite-dimensional. In this note, we confirm this for Banach
algebras acting on Banach spaces with the uniform approximation property. This
generalizes a result of Paulsen and Smith who proved the same for Banach
algebras acting on Hilbert spaces.

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