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A note on B*-algebras

Published online by Cambridge University Press:  24 October 2008

G. R. Allan
Affiliation:
Sidney Sussex College, Cambridge

Extract

A normed algebra A is a pre-B*-algebra if its norm satisfies ∥x*x∥= ∥x2 for all elements x ∈ A; if A is also complete in its norm, then A is a B*-algebra (see (l), page 180). In the study of certain locally convex algebras, the problem arose of expressing the condition that an algebra be a pre-B*-algebra in terms of its properties as a locally convex algebra, rather than in terms of the norm. A solution to this problem is presented in this note; the application to the theory of locally convex algebras will appear elsewhere.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

REFERENCE

(1)Rickart, C. E.The general theory of Banach algebras (Van Nostrand; 1960).Google Scholar