On polynomially bounded operators with shift-type invariant subspaces

Abstract

Generalizing a particular case of a result by Kerchy (2007) for contractions, the following was proved by the author: if T is a polynomially bounded operator and there exists a transformation with dense range which intertwines T with the bilateral shift of multiplicity 1, then there exists an invariant subspace M of T such that T|M is similar to the unilateral shift of multiplicity 1. In the present paper, several corollaries of this result are given. In particular, reflexivity of polynomially bounded operators described above is proved.