A remark on continuity of positive linear functionals on separable Banach *-algebras

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.

arXiv comment3 pages