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 in:Complex analysis and operator theory 2018-04, Vol.12 (4), p.931-943
Main Author: Pal, Sourav
Format: Article
Language:English
Subjects:
Analysis
Decomposition
Mathematics
Mathematics and Statistics
Operator Theory
Operators
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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