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Boundedness and completeness in locally convex spaces and algerbras

Published online by Cambridge University Press:  09 April 2009

Gerard A. Joseph
Gerard A. Joseph
Affiliation:
Department of Mathematics, University of Newcastle, New South Wales, 2308, Australia
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Abstract

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The set of bounded elements of a unital l.m.c. algebra is characterised as the union of certain naturally defined normed subalgebras, and an analogous characterisation is given for algebras of quotient-bounded operators on a locally convex space. Pseudocomplete l.m.c. algebras are characterised in terms of the completeness of these subalgebras, and the equivalence of this condition with the pseudocompleteness of the quotient-bounded operator algebras established. The scalar multiples of the identity in a unital l.m.c. algebra are characterised in terms of certain boundedness conditions.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 1 , August 1977 , pp. 50 - 63
Copyright
Copyright © Australian Mathematical Society 1977

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