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Cohen elements in Banach algebras*†

Published online by Cambridge University Press:  14 November 2011

Allan M. Sinclair
Allan M. Sinclair
Affiliation:
Department of Mathematics, University of California, Los Angeles, California 90024, U.S.A. Department of Mathematics, University of Edinburgh, Edinburgh, Scotland
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Synopsis

The definition of Cohen elements in a commutative Banach algebra with a countable bounded approximate identity given by Esterle is modified slightly to be more analogous to the invertible elements in a unital Banach algebra. With the modified definition the n1-Cohen factorization results that were proved by Esterle are shown tohold in the semigroup of Cohen elements. If is the algebra of continuous complex valued functions vanishing at infinity on a σ-compact locally compact Hausdorff space X, then the Cohen elements in are identified and a natural quotient of a subsemigroup of Cohen elements is shown to be a group, isomorphic to the abstract index group of C(X∪{∞}).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 84 , Issue 1-2 , 1979 , pp. 55 - 70
Copyright
Copyright © Royal Society of Edinburgh 1979

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