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Representability of invariant positive sesquilinear forms on partial *-algebras

Published online by Cambridge University Press:  24 October 2008

J.-P. Antoine  and
A. Inoue
J.-P. Antoine
Affiliation:
Institut de Physique Théorique, Université Catholique de Louvain, B-1348-Louvain-la-Neuve, Belgique
A. Inoue
Affiliation:
Department of Applied Mathematics, Fukuoka University, Fukuoka, Japan
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Abstract

We consider invariant positive sesquilinear forms on a (partial) *-algebra A without unit. First we investigate the relationship between extendability and representability for such a form ø; in particular we discuss under which conditions the two concepts are equivalent. Then we introduce the notions of weak representability and strict unrepresentability, and we show that every fully invariant positive sesquilinear form on A × A is uniquely decomposed into a weakly representable part and a strictly unrepresentable part.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 2 , September 1990 , pp. 337 - 353
Copyright
Copyright © Cambridge Philosophical Society 1990

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