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Approximate identities in extensions of topologically nilpotent Banach algebras

Published online by Cambridge University Press:  14 November 2011

P. G. Dixon
Affiliation:
Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH, U.K.
G. A. Willis
Affiliation:
Centre for Mathematics and its Applications, Australian National University, G.P.O. Box 4, Canberra, ACT 2601, Australia

Synopsis

In commutative Banach algebras with factorisation, the existence of an identity (bounded approximate identity) modulo a topologically nilpotent radical implies the existence of a global identity (bounded approximate identity), respectively.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1992

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References

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4Rickart, C. E.. General theory of Banach algebras (Princeton: van Nostrand, 1960).Google Scholar
5Willis, G.. Examples of factorization without bounded approximate units. Proc. London Math. Soc. (to appear).Google Scholar