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arXiv · 1708.00724

Canonical decomposition of operators associated with the symmetrized polydisc

Sourav Pal
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Abstract

A tuple of commuting operators $(S_1,\dots,S_{n-1},P)$ for which the closed symmetrized polydisc $\Gamma_n$ is a spectral set is called a $\Gamma_n$-contraction. We show that every $\Gamma_n$-contraction admits a decomposition into a $\Gamma_n$-unitary and a completely non-unitary $\Gamma_n$-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 $\Gamma_n$ and $\Gamma_n$-contractions.

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Sourav Pal. 2017-08-02. Canonical decomposition of operators associated with the symmetrized polydisc. https://arxiv.org/abs/1708.00724

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