Algebras of subnormal operators

Abstract

The paper deals with the following: (I) If S is a subnormal operator on H , then Ol (S) = W (S) = Alg Lat S. (II) If L ∈ ( Ol (S), σ-wot) ∗, then there exist vectors a and b in H such that L( T) = 〈 T a, b〉 for every T in Ol . (III) In addition to I the map i( T) = T is a homeomorphism from ( Ol , σ-wot) onto ( W (S), wot). (IV) If S is not a reductive normal operator, then there exists a cyclic invariant subspace for S that has an open set of bounded point evaluations. (This open set can be constructed to be as large as possible.)