Canonical decomposition of operators associated with the symmetrized polydisc

Sourav Pal

Canonical decomposition of operators associated with the symmetrized polydisc

Functional Analysis 2017-09-19 v2

Authors: Sourav Pal

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.

Keywords

symmetrized polydisc spectral set Gamma_n-contraction canonical decomposition unitary operator completely non-unitary contraction operator theory

Cite

@article{arxiv.1708.00724,
  title  = {Canonical decomposition of operators associated with the symmetrized polydisc},
  author = {Sourav Pal},
  journal= {arXiv preprint arXiv:1708.00724},
  year   = {2017}
}

Comments

Complex Analysis and Operator Theory, Published online on August 28, 2017. arXiv admin note: text overlap with arXiv:1610.00936

Canonical decomposition of operators associated with the symmetrized polydisc

Abstract

Keywords

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