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On the strong radical of certain Banach algebras

Published online by Cambridge University Press:  20 January 2009

Bertram Yood
Bertram Yood
Affiliation:
Pennsylvania State University, University Park, PA. 16802, U.S.A..
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Let A be a complex Banach algebra. By an ideal in A we mean a two-sided idealunless otherwise specified. As in (7, p. 59) by the strong radical of A we mean theintersection of the modular maximal ideals of A (if there are no such ideals we set =A). Our aim is to discuss the nature of and the relation of to A for a specialclass of Banach algebras. Henceforth A will denote a semi-simple modular annihilatorBanach algebra (one for which the left (right) annihilator of each modular maximalright (left) ideal is not (0)). For the theory of such algebras see (2) and (9).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 21 , Issue 1 , March 1978 , pp. 81 - 85
Copyright
Copyright © Edinburgh Mathematical Society 1978

References

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