The uniform and the strong topology on realizations of the algebra of polynomials

Abstract

It is shown that under quite general assumptions on the operators A 1,…, A n (unbounded, symmetric) and on the domain D on the realization P(A 1,…,A n) of the algebra of polynomials P(x 1,…,x n) , the strongest locally convex topology τ st coincides with the uniform topology τ D as well as with the strong operator topology τ s. In the case n = 2 some conditions are given, under which these general assumptions are fulfilled.