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Quotient bounded elements in locally convex algebras

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  09 April 2009

Subhash J. Bhatt
Subhash J. Bhatt
Affiliation:
Dapartment of Mathematics Sardar Patel UniversityVallabh Vidyanagar-388120 Gujarat, India
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Abstract

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The quotient bounded and the universally bounded elements in a calibrated locally convex algebra are defined and studied. In the case of a generalized B*-algebra A, they are shown to form respectively b* and B*-algebras, both dense in A. An internal spatial characterization of generalized B*-algebras is obtained. The concepts are illustrated with the help of examples of algebras of measurable functions and of continuous linear operators on a locally convex space.

MSC classification

Secondary: 46H05: General theory of topological algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 1 , August 1982 , pp. 102 - 113
Copyright
Copyright © Australian Mathematical Society 1982

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