A note on partial*–algebras and spaces of distributions

Abstract

Given a rigged Hilbert space (D,H,D'), the spaces D_{loc are considered. It is shown that, if D is a Hilbert *-algebra, D_{loc} carry out a natural structure of partial *-algebra. Furthermore, on D_{loc} it is defined a topology, so that D_{loc} is an interspace. Examples from distributions theory are considered.