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
Recommended Citation
Chattopadhyay, Arup; Das, B. Krishna; and Sarkar, Jaydeb, "Inner multipliers and Rudin type invariant subspaces" (2016). Journal Articles. 4264.
https://digitalcommons.isical.ac.in/journal-articles/4264
