Similarity of n-hypercontractions and backward Bergman shifts

Ronald G. Douglas; Hyun Kyoung Kwon; Sergei Treil

doi:10.1112/jlms/jdt035

Similarity of n-hypercontractions and backward Bergman shifts

Ronald G. Douglas
, Hyun Kyoung Kwon
, Sergei Treil

Mathematics and Statistics

University at Albany

Texas A&M University
Brown University

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

We give a necessary and sufficient condition for an n-hypercontraction to be similar to the backward shift operator on a weighted Bergman space. This characterization serves as a generalization of the description given in the Hardy space setting, where the geometry of the eigenvector bundles of the operators is used.

Original language	English
Pages (from-to)	637-648
Number of pages	12
Journal	Journal of the London Mathematical Society
Volume	88
Issue number	3
DOIs	https://doi.org/10.1112/jlms/jdt035
State	Published - Dec 2013

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title = "Similarity of n-hypercontractions and backward Bergman shifts",

abstract = "We give a necessary and sufficient condition for an n-hypercontraction to be similar to the backward shift operator on a weighted Bergman space. This characterization serves as a generalization of the description given in the Hardy space setting, where the geometry of the eigenvector bundles of the operators is used.",

author = "Douglas, \{Ronald G.\} and Kwon, \{Hyun Kyoung\} and Sergei Treil",

year = "2013",

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AU - Kwon, Hyun Kyoung

AU - Treil, Sergei

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N2 - We give a necessary and sufficient condition for an n-hypercontraction to be similar to the backward shift operator on a weighted Bergman space. This characterization serves as a generalization of the description given in the Hardy space setting, where the geometry of the eigenvector bundles of the operators is used.

AB - We give a necessary and sufficient condition for an n-hypercontraction to be similar to the backward shift operator on a weighted Bergman space. This characterization serves as a generalization of the description given in the Hardy space setting, where the geometry of the eigenvector bundles of the operators is used.

UR - https://www.scopus.com/pages/publications/84890161405

U2 - 10.1112/jlms/jdt035

DO - 10.1112/jlms/jdt035

M3 - Article

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SP - 637

EP - 648

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 3

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Similarity of n-hypercontractions and backward Bergman shifts

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