Curvature condition for non-contractions does not imply similarity to the backward shift

Hyun Kyoung Kwon; Sergei Treil

doi:10.1007/s00020-010-1761-3

Curvature condition for non-contractions does not imply similarity to the backward shift

Hyun Kyoung Kwon
, Sergei Treil

Mathematics and Statistics

University at Albany

Seoul National University

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

2 Scopus citations

Abstract

We give an example of an operator that satisfies the curvature condition as defined in Kwon and Treil (Publ Mat 53(2):417-438, 2009), but is not similar to the backward shift S* on the Hardy class H². We conclude therefore that the contraction assumption in the similarity characterization given in Kwon and Treil (Publ Mat 53(2): 417-438, 2009) is a necessary requirement.

Original language	English
Pages (from-to)	529-538
Number of pages	10
Journal	Integral Equations and Operator Theory
Volume	66
Issue number	4
DOIs	https://doi.org/10.1007/s00020-010-1761-3
State	Published - Apr 2010

Keywords

Backward shift
Carleson measure
Curvature condition
Eigenvector bundle
Similarity

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10.1007/s00020-010-1761-3

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title = "Curvature condition for non-contractions does not imply similarity to the backward shift",

abstract = "We give an example of an operator that satisfies the curvature condition as defined in Kwon and Treil (Publ Mat 53(2):417-438, 2009), but is not similar to the backward shift S* on the Hardy class H2. We conclude therefore that the contraction assumption in the similarity characterization given in Kwon and Treil (Publ Mat 53(2): 417-438, 2009) is a necessary requirement.",

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AU - Kwon, Hyun Kyoung

AU - Treil, Sergei

PY - 2010/4

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N2 - We give an example of an operator that satisfies the curvature condition as defined in Kwon and Treil (Publ Mat 53(2):417-438, 2009), but is not similar to the backward shift S* on the Hardy class H2. We conclude therefore that the contraction assumption in the similarity characterization given in Kwon and Treil (Publ Mat 53(2): 417-438, 2009) is a necessary requirement.

AB - We give an example of an operator that satisfies the curvature condition as defined in Kwon and Treil (Publ Mat 53(2):417-438, 2009), but is not similar to the backward shift S* on the Hardy class H2. We conclude therefore that the contraction assumption in the similarity characterization given in Kwon and Treil (Publ Mat 53(2): 417-438, 2009) is a necessary requirement.

KW - Backward shift

KW - Carleson measure

KW - Curvature condition

KW - Eigenvector bundle

KW - Similarity

UR - https://www.scopus.com/pages/publications/77951824234

U2 - 10.1007/s00020-010-1761-3

DO - 10.1007/s00020-010-1761-3

M3 - Article

SN - 0378-620X

VL - 66

SP - 529

EP - 538

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 4

ER -

Curvature condition for non-contractions does not imply similarity to the backward shift

Abstract

Keywords

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