Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-24T17:03:26.682Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on B*-algebras

Published online by Cambridge University Press:  24 October 2008

G. R. Allan
G. R. Allan
Affiliation:
Sidney Sussex College, Cambridge
Get access Rights & Permissions [Opens in a new window]

Extract

A normed algebra A is a pre-B*-algebra if its norm satisfies ∥x*x∥= ∥x∥2 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
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 1 , January 1965 , pp. 29 - 32
Copyright
Copyright © Cambridge Philosophical Society 1965

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCE

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