Journal of Operator Theory
Volume 84, Issue 1, Summer 2020 pp. 3-34.
On existence of shift-type invariant subspaces for polynomially bounded operators
Authors:
Maria F. Gamal'
Author institution:St. Petersburg Branch, V.A. Steklov Institute
of Mathematics, Russian Academy of Sciences, Fontanka 27, St. Petersburg,
191023, Russia
Summary: A very particular case of results by K\'erchy (2007) is as follows. Let the unitary asymptote of a contraction $T$
contain 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 $1$.
The proof is based on the Sz.-Nagy--Foias functional model for contractions.
In the present paper this result is generalized to polynomially bounded operators. The proof is based on a result by Bourgain (1984).
DOI: http://dx.doi.org/10.7900/jot.2018dec08.2250
Keywords: shift-type invariant subspace, polynomially bounded operator, similarity, unilateral shift
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