Canonical decomposition of operators associated with the symmetrized\n polydisc

2017/08/02 by Sourav Pal, Pal, Sourav
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1708.00724

openalex publication_date 2017/08/02 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

A tuple of commuting operators (S₁,\…,S_n-1,P) for which the closed\nsymmetrized polydisc \Γ_n is a spectral set is called a\n\Γ_n-contraction. We show that every \Γ_n-contraction admits a\ndecomposition into a \Γ_n-unitary and a completely non-unitary\n\Γ_n-contraction. This decomposition is an analogue to the canonical\ndecomposition of a contraction into a unitary and a completely non-unitary\ncontraction. We also find new characterizations for the set \Γ_n and\n\Γ_n-contractions.\n

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