On polynomially bounded operators with shift-type invariant subspaces

Abstract

A particular case of [07] was generalized from contractions to polynomially bounded operators in [G19]. Namely, it is proved in [G19] that if the unitary asymptote of a polynomially bounded operator $T$ contains the bilateral shift of multiplicity $1$, then there exists an invariant subspace $\mathcal{M}$ of $T$ such that $T{|}_{\mathcal{M}}$ is similar to the unilateral shift of multiplicity $1$. In the present paper, some corollaries of this result are given. In particular, reflexivity of polynomially bounded operators described above is proved.

Original proof is simplified. Additional results are added. Parts of arXiv:1803.03626v2 and arXiv:1812.01419v1 not published and submitted to journals are repeated

References in corpus (2)

• Quasianalytic polynomially bounded operators
• On existence of shift-type invariant subspaces for polynomially bounded operator

Cited by in corpus (1)

• On similarity to contractions of class $C_{\cdot 0}$ with finite defects