Characterization of invariant subspaces in the polydisc

Article Type

Research Article

Publication Title

Journal of Operator Theory

Abstract

We give a complete characterization of invariant subspaces for (Mz1, . . ., Mzn) on the Hardy space H2(D[double-struck]n) over the unit polydisc D[double-struck]n in ℂn, n > 1. In particular, this yields a complete set of unitary invariants for invariant subspaces for (Mz1, . . ., Mzn) on H2(D[double-struck]n). As a consequence, we classify a large class of n-tuples of commuting isometries. All of our results hold for vector-valued Hardy spaces over Dn, n > 1.

First Page

445

Last Page

468

DOI

10.7900/jot.2018jun07.2204

Publication Date

1-1-2019

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