Robert F. Olin

Algebras of subnormal operators

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.)

Cellular-indecomposable subnormal operators

A bounded operator T is cellular-indecomposable if LnM≠{0} whenever L and M are any two nonzero invariant subspaces for T. We show that any such subnormal operator has a cyclic normal extension and is unitarily equivalent modulo the compact operators to an analytic Toeplitz operator whose symbol is a weak-star generator of H∞.