Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Arens multiplication and a characterization of $ w\sp{\ast} $-algebras


Author: T. W. Palmer
Journal: Proc. Amer. Math. Soc. 44 (1974), 81-87
MSC: Primary 46L10
MathSciNet review: 0341122
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \mathfrak{A}$ be a Banach algebra which is the dual of a normed linear space $ \mathfrak{X}$. Suppose the multiplication in $ \mathfrak{A}$ is a continuous function of each factor separately in the weak* topology. We show that the natural projection of $ {\mathfrak{A}^{ \ast \ast }} = {\mathfrak{X}^{ \ast \ast \ast }}$ onto $ \mathfrak{A} = {\mathfrak{X}^ \ast }$ is a homomorphism with respect to either Arens' multiplication. From this we derive a simple proof of a variant form of Sakai's characterization of $ {W^ \ast }$-algebras.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L10

Retrieve articles in all journals with MSC: 46L10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0341122-8
Article copyright: © Copyright 1974 American Mathematical Society