A note on B*-algebras
Published online by Cambridge University Press: 24 October 2008
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
References
REFERENCE
- 4
- Cited by