Canonical Decomposition of Operators Associated with the Symmetrized Polydisc

A tuple of commuting operators ( S 1 , ⋯ , S n - 1 , P ) for which the closed symmetrized polydisc Γ n is a spectral set is called a Γ n -contraction. We show that every Γ n -contraction admits a decomposition into a Γ n -unitary and a completely non-unitary Γ n -contraction. This decomposition is a...

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Bibliographic Details
Published inComplex analysis and operator theory Vol. 12; no. 4; pp. 931 - 943
Main Author Pal, Sourav
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2018
Springer Nature B.V
Subjects
Analysis
Decomposition
Mathematics
Mathematics and Statistics
Operator Theory
Operators
Symmetrized polydisc
47A15
Canonical decomposition
47A13
47A25
Spectral set
47A45
47A20
Contraction
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Summary:A tuple of commuting operators ( S 1 , ⋯ , S n - 1 , P ) for which the closed symmetrized polydisc Γ n is a spectral set is called a Γ n -contraction. We show that every Γ n -contraction admits a decomposition into a Γ n -unitary and a completely non-unitary Γ n -contraction. This decomposition is an analogue to the canonical decomposition of a contraction into a unitary and a completely non-unitary contraction. We also find new characterizations for the set Γ n and Γ n -contractions.
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-017-0721-1