A real seminorm with square property is submultiplicative

A seminorm with square property on a real associative algebra is submultiplicativeComment: 3 page

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.Comment: 3 page

Positive linear functionals on BP*-algebras

Let A be a BP*-algebra with identity e, P_{1}(A) be the set of all positive linear functionals f on A such that f(e) = 1, and let M_{s}(A) be the set of all nonzero hermitian multiplicative linear functionals on A. We prove that M_{s}(A) is the set of extreme points of P_{1}(A). We also prove that, if M_{s}(A) is equicontinuous, then every positive linear functional on A is continuous. Finally, we give an example of a BP*-algebra whose topological dual is not included in the vector space generated by P_{1}(A), which gives a negative answer to a question posed by M. A. Hennings.Comment: This is an English translation of the original article written in Frenc