The reducibility of compressed shifts on Beurling type quotient modules over the bidisk

Zhu, Senhua; Yang, Yichuan; Lu, Yufeng

doi:10.1016/j.jfa.2019.108304

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Notation and Preliminaries1

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2023

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Cited by 7 publications

(2 citation statements)

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“…part. This the content of [Lemma 2.2, [32]] which states that for a c.n.u. contraction T ∈ B(H) we always have…”

Section: Notation and Preliminariesmentioning

confidence: 99%

Pairs of Commuting Pure Contractions and Isometric dilation

Sarkar

2021

Preprint

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A particular case of the fundamental Sz.-Nagy-Foias functional model for a contraction states that a pure contraction always dilates to a pure isometry. We are interested in the similar question for pairs, more precisely: does a pair of commuting pure contractions always dilate to a pair of commuting pure isometries? The purpose of this article is to identify pairs of commuting pure contractions for which the above question has an affirmative answer. Our method is based on an explicit structure of isometric dilation for pure pairs of commuting contractions obtained in a recent work by Das, Sarkar and the author.

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“…part. This the content of [Lemma 2.2, [32]] which states that for a c.n.u. contraction T ∈ B(H) we always have…”

Section: Notation and Preliminariesmentioning

confidence: 99%

Pairs of Commuting Pure Contractions and Isometric dilation

Sarkar

2021

Preprint

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“…We refer the reader to the papers [4,9,16] and the survey [15] for other results (mostly in two variables) on Beurling quotient modules.…”

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confidence: 99%

Beurling quotient modules on the polydisc

Bhattacharjee¹,

Das²,

Debnath³

et al. 2021

Preprint

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Let H 2 (D n ) denote the Hardy space over the polydiscWe present two applications: first, we obtain a dilation theorem for Brehmer n-tuples of commuting contractions, and, second, we relate joint invariant subspaces with factorizations of inner functions. All results work equally well for general vector-valued Hardy spaces. Contents 1. Introduction 1 2. Proof of Theorem 1.1 4 3. Isometric dilations 9 4. Factorizations and invariant subspaces 10 References 14

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The Agler Reducing Subspace for the Operator-Valued Inner Function Over the Bidisk

Zhu

Yang

2022

Integr. Equ. Oper. Theory

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The reducibility of compressed shifts on Beurling type quotient modules over the bidisk

Cited by 7 publications

References 15 publications

Pairs of Commuting Pure Contractions and Isometric dilation

Pairs of Commuting Pure Contractions and Isometric dilation

Beurling quotient modules on the polydisc

The Agler Reducing Subspace for the Operator-Valued Inner Function Over the Bidisk

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