Reflexivity of an extension of a sub-normal operator by algebraic operator

摘要

A bounded linear operator on a Hilbert space is said to be reflexive if the operators which leave invariant the invariant subspaces of T are wot-limits of polynomials in T . In this paper we give a necessary and sufficient condition for an extension of a subnormal operator by an algebraic one to be reflexive.We also give a formula for the reflexivity defect of such extensions.