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Sufficient conditions for the projective freeness of Banach algebras

Brudnyi, Alexander and Sasane, Amol (2009) Sufficient conditions for the projective freeness of Banach algebras. Journal of Functional Analysis, 257 (12). pp. 4003-4014. ISSN 0022-1236

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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.

Item Type: Article
Official URL: http://www.elsevier.com/wps/find/journaldescriptio...
Additional Information: © 2009 Elsevier Inc.
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 31 Mar 2010 11:31
URL: http://eprints.lse.ac.uk/27648/

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