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The weak density of the non-invertible elements of a commutative Banach algebra

Published online by Cambridge University Press:  17 April 2009

Colin C. Graham
Colin C. Graham
Affiliation:
Northwestern University, Evanston, Illinois, USA.
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Abstract

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This is proved: if B is a commutative Banach algebra with identity, then the non-invertible elements of B are weakly dense in B if and only if the maximal ideal space of B is infinite.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 2 , April 1971 , pp. 179 - 182
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Gamelin, Theodore W., Uniform algebras (Prentice-Hall, Englewood Cliffs, New Jersey, 1969).Google Scholar
[2]Gray, J.D., “The weak closure of the set of singular elements in a Banach algebra”, Bull. Austral. Math. Soc. 2 (1970), 89–93.CrossRefGoogle Scholar
[3]Kelley, J.L., Namioka, Isaac and Donoghue, W.F. Jr, Lucas, Kenneth R., Pettis, B.J., Poulsen, Ebbe Thue, Price, G. Baley, Robertson, Wendy, Scott, W.R., Smith, Kennan T., Linear topological spaces (Van Kostrand, Princeton, New Jersey; Toronto; New York; London; 1963).CrossRefGoogle Scholar
[4]Rickart, Charles E., General theory of Banach algebras (Van Nostrand, Princeton, New Jersey; Toronto; London; New York; 1960).Google Scholar