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
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.
|Additional Information:||© 2009 Elsevier Inc.|
|Uncontrolled Keywords:||Projective free ring, Banach algebra, Maximal ideal space|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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