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The weak closure of the set of singular elements in a Banach algebra

Published online by Cambridge University Press:  17 April 2009

J.D. Gray
J.D. Gray
Affiliation:
University of New South Wales, Kensington, New South Wales.
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Abstract

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In this note it is proved that for a certain class of infinite dimensional Banach algebras the set of singular elements (the non-units) is dense in the weak topology.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 2 , Issue 1 , February 1970 , pp. 89 - 93
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Dunford, Nelson and Schwartz, Jacob T., Linear operators. Part I (Interscience Publishers, New York, London, 1958).Google Scholar
[2]Rickart, Charles E., General theory of Banach algebras, (Van Nostrand, Princeton, New Jersey, 1960).Google Scholar