A Remark on Continuity of Positive Linear Functionals on Separable Banach *-Algebras

M. El Azhari

doi:10.2478/awutm-2013-0011

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A Remark on Continuity of Positive Linear Functionals on Separable Banach *-Algebras

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 51 (2013): Issue 2 (December 2013)

By: M. El Azhari

Open Access

|Jan 2014

Abstract

Using a variation of the Murphy-Varopoulos Theorem, we give a new proof of the following R. J. Loy Theorem: Let A be a separable Banach _*-algebra with center Z such that ZA has at most countable codimension, then every positive linear functional on A is continuous.

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