Canonical decomposition of operators associated with the symmetrized polydisc
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Publication:6289694
DOI10.1007/S11785-017-0721-1arXiv1708.00724MaRDI QIDQ6289694
Publication date: 2 August 2017
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.
Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Invariant subspaces of linear operators (47A15) Dilations, extensions, compressions of linear operators (47A20) Canonical models for contractions and nonselfadjoint linear operators (47A45) Spectral sets of linear operators (47A25)
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