Algebras of subnormal operators

The paper deals with the following: (I) If S is a subnormal operator on $\text{H}$, then $\text{Ol}$(S) = $\text{W}$(S) = Alg Lat S. (II) If L ∈ ($\text{Ol}$(S), σ-wot)¹, then there exist vectors a and b in $\text{H}$ such that L(T) = 〈Ta, b〉 for every T in $\text{Ol}$. (III) In addition to I the map i(T) = T is a homeomorphism from ($\text{Ol}$, σ-wot) onto ($\text{W}$(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.)