Inner multipliers and Rudin type invariant subspaces

被引：0
|
作者：
Chattopadhyay A. [1 ]
Das B.K. [2 ]
Sarkar J. [3 ]
机构：
[1] Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati
[2] Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbaii
[3] Indian Statistical Institute, Statistics and Mathematics Unit, 8th Mile, Mysore Road, Bangalore
来源：
Acta Scientiarum Mathematicarum | 2016年 / 82卷 / 3-4期
关键词：
Hardy space; Inner sequence; Invariant subspace; Operator-valued inner function; Unitary equivalence;
D O I：
10.14232/actasm-015-773-y
中图分类号：
学科分类号：
摘要：
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). © 2016 Bolyai Institute, University of Szeged.
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页码：519 / 528
页数：9
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