ESMAEIL ANSARI-PIRI - Department of Mathematics, Guilan University, Rasht, Iran

The well known simple relation between the norm of an element x and xx* in a C* −algebra has a high potential and is too much important. In this note we try to extend this relation to metrizable -not necessarily locally convex - star algebras. Using the new equivalent definition in the absence of norms and semi-norms we get some simple results.

Involution topological algebras, star topological algebras, C* −algebras