Journal of Operator Theory

Volume 34, Issue 1, Summer 1995 pp. 125-144.

Spaces contractively invariant for the backward shift

Authors: Michael Sand
Author institution:Department of Mathematics, University of California, Riverside CA 92521, U.S.A.

Summary: We classify those Hilbert spaces, contractively contained in a vector-valued H^2-space, that are carried into themselves contractively by the backward shift. We then show when a completely non-unitary operator is unitarily equivalent to the action of the backward shift on one of its contractively invariant spaces.

Keywords: Shifts, Hardy spaces, contractively contained spaces, invariant spaces.

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