The trace of the curvature determines similarity

Yingli Hou; Kui Ji; Hyun Kyoung Kwon

doi:10.4064/sm8588-9-2016

The trace of the curvature determines similarity

Yingli Hou
, Kui Ji
, Hyun Kyoung Kwon

Mathematics and Statistics

University at Albany

Hebei Normal University

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

17 Scopus citations

Abstract

We prove that the quantity that appears in a recent similarity characterization for Cowen-Douglas operators is the trace of the curvature of the eigenvector bundle. This gives the first geometric interpretation of the similarity of operators.

Original language	English
Pages (from-to)	193-200
Number of pages	8
Journal	Studia Mathematica
Volume	236
Issue number	2
DOIs	https://doi.org/10.4064/sm8588-9-2016
State	Published - 2017

Keywords

Cowen-Douglas operator
Curvature
Eigenvector bundle
Similarity
Subharmonic function

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10.4064/sm8588-9-2016

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title = "The trace of the curvature determines similarity",

abstract = "We prove that the quantity that appears in a recent similarity characterization for Cowen-Douglas operators is the trace of the curvature of the eigenvector bundle. This gives the first geometric interpretation of the similarity of operators.",

keywords = "Cowen-Douglas operator, Curvature, Eigenvector bundle, Similarity, Subharmonic function",

author = "Yingli Hou and Kui Ji and Kwon, \{Hyun Kyoung\}",

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year = "2017",

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T1 - The trace of the curvature determines similarity

AU - Hou, Yingli

AU - Ji, Kui

AU - Kwon, Hyun Kyoung

PY - 2017

Y1 - 2017

N2 - We prove that the quantity that appears in a recent similarity characterization for Cowen-Douglas operators is the trace of the curvature of the eigenvector bundle. This gives the first geometric interpretation of the similarity of operators.

AB - We prove that the quantity that appears in a recent similarity characterization for Cowen-Douglas operators is the trace of the curvature of the eigenvector bundle. This gives the first geometric interpretation of the similarity of operators.

KW - Cowen-Douglas operator

KW - Curvature

KW - Eigenvector bundle

KW - Similarity

KW - Subharmonic function

UR - https://www.scopus.com/pages/publications/85017436819

U2 - 10.4064/sm8588-9-2016

DO - 10.4064/sm8588-9-2016

M3 - Article

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VL - 236

SP - 193

EP - 200

JO - Studia Mathematica

JF - Studia Mathematica

IS - 2

ER -

The trace of the curvature determines similarity

Abstract

Keywords

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