Inner multipliers and Rudin type invariant subspaces

Article Type

Research Article

Publication Title

Acta Scientiarum Mathematicarum

Abstract

Let ϵ be a Hilbert space and H2ϵ(D) be the ϵ-valued Hardy space over the unit disc D in ℂ. The well-known Beurling-Lax-Halmos theorem states that every shift invariant subspace of H2ϵ(D) other than {0} has the form ΘH2ϵ(D), where Θ is an operator-valued inner multiplier in H1B(ϵ∗;ϵ)(D) for some Hilbert space ϵ∗. In this paper we identify H2(Dn) with the H2(Dn-1)-valued Hardy space H2H2(Dn-1)(D) and classify all such inner multipliers Θ ∈ H∞B(H2(Dn-1))(D) for which ΘH2H2(Dn-1)(D) is a Rudin type invariant subspace of H2(Dn).

First Page

519

Last Page

528

DOI

10.14232/actasm-015-773-y

Publication Date

1-1-2016

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