On unitary equivalence of compact operator tuples

Wei He; Rongwei Yang

doi:10.1007/s11425-021-1976-8

On unitary equivalence of compact operator tuples

Wei He
, Rongwei Yang

Mathematics and Statistics

University at Albany

Southeast University, Nanjing

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

3 Scopus citations

Abstract

For a compact operator tuple A, if its projective spectrum P(A_*) is smooth, there exists a natural Hermitian holomorphic line bundle E_A over P(A_*) which is a unitary invariant for A. This paper shows that under some additional spectral conditions, E_A is a complete unitary invariant, i.e., E_A can determine the compact operator tuple up to unitary equivalence.

Original language	English
Pages (from-to)	571-580
Number of pages	10
Journal	Science China Mathematics
Volume	66
Issue number	3
DOIs	https://doi.org/10.1007/s11425-021-1976-8
State	Published - Mar 2023

Keywords

47A13
Hermitian holomorphic bundle
compact operator tuple
projective spectrum
unitary equivalence

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10.1007/s11425-021-1976-8

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title = "On unitary equivalence of compact operator tuples",

abstract = "For a compact operator tuple A, if its projective spectrum P(A*) is smooth, there exists a natural Hermitian holomorphic line bundle EA over P(A*) which is a unitary invariant for A. This paper shows that under some additional spectral conditions, EA is a complete unitary invariant, i.e., EA can determine the compact operator tuple up to unitary equivalence.",

keywords = "47A13, Hermitian holomorphic bundle, compact operator tuple, projective spectrum, unitary equivalence",

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AB - For a compact operator tuple A, if its projective spectrum P(A*) is smooth, there exists a natural Hermitian holomorphic line bundle EA over P(A*) which is a unitary invariant for A. This paper shows that under some additional spectral conditions, EA is a complete unitary invariant, i.e., EA can determine the compact operator tuple up to unitary equivalence.

KW - 47A13

KW - Hermitian holomorphic bundle

KW - compact operator tuple

KW - projective spectrum

KW - unitary equivalence

UR - https://www.scopus.com/pages/publications/85137910772

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DO - 10.1007/s11425-021-1976-8

M3 - Article

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VL - 66

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EP - 580

JO - Science China Mathematics

JF - Science China Mathematics

IS - 3

ER -

On unitary equivalence of compact operator tuples

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Keywords

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