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

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.