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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  and
G. A. Willis
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
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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
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 122 , Issue 1-2 , 1992 , pp. 45 - 52
Copyright
Copyright © Royal Society of Edinburgh 1992

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References

1Dixon, P. G.. Factorization and unbounded approximate identities in Banach algebras. Math. Proc. Cambridge Philos. Soc. 107 (1990), 557–571.CrossRefGoogle Scholar
2Dixon, P. G.. Topologically nilpotent Banach algebras and factorisation. Proc. Roy. Soc. Edinburgh Sect. A 119 (1991), 329–341.CrossRefGoogle Scholar
3Doran, R. S. and Wichmann, J.. Approximate identities and factorization in Banach modules. Lecture Notes in Mathematics 768 (Berlin: Springer, 1979).Google Scholar
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