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Sufficient conditions for the projective freeness of Banach algebras

By Alexander Brudnyi and Amol Sasane

Abstract

Let R be a unital semi-simple commutative complex Banach algebra, and let M(R) denote its maximal ideal space, equipped with the Gelfand topology. Sufficient topological conditions are given on M(R) for R to be a projective free ring, that is, a ring in which every finitely generated projective R-module is free. Several examples are included, notably the Hardy algebra H∞(X) of bounded holomorphic functions on a Riemann surface of finite type, and also some algebras of stable transfer functions arising in control theory

Topics: QA Mathematics
Publisher: Academic Press
Year: 2009
DOI identifier: 10.1016/j.jfa.2009.05.003
OAI identifier: oai:eprints.lse.ac.uk:27648
Provided by: LSE Research Online
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