Canonical Decomposition of Operators Associated with the Symmetrized Polydisc

Sourav Pal

doi:10.1007/s11785-017-0721-1

Canonical Decomposition of Operators Associated with the Symmetrized Polydisc

Sourav Pal

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

A tuple of commuting operators (S₁, ⋯ , 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.

Original language	English
Pages (from-to)	931-943
Number of pages	13
Journal	Complex Analysis and Operator Theory
Volume	12
Issue number	4
DOIs	https://doi.org/10.1007/s11785-017-0721-1
State	Published - 1 Apr 2018
Externally published	Yes

Keywords

Canonical decomposition
Spectral set
Symmetrized polydisc
Γ -Contraction

ASJC Scopus subject areas

Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

Access to Document

10.1007/s11785-017-0721-1

Cite this

@article{5c4b9933d03c444c96b3f702fc5224bf,

title = "Canonical Decomposition of Operators Associated with the Symmetrized Polydisc",

abstract = "A tuple of commuting operators (S1, ⋯ , Sn-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.",

keywords = "Canonical decomposition, Spectral set, Symmetrized polydisc, Γ -Contraction",

author = "Sourav Pal",

note = "Publisher Copyright: {\textcopyright} 2017, Springer International Publishing AG.",

year = "2018",

month = apr,

day = "1",

doi = "10.1007/s11785-017-0721-1",

language = "English",

volume = "12",

pages = "931--943",

journal = "Complex Analysis and Operator Theory",

issn = "1661-8254",

publisher = "Springer International Publishing",

number = "4",

}

TY - JOUR

T1 - Canonical Decomposition of Operators Associated with the Symmetrized Polydisc

AU - Pal, Sourav

PY - 2018/4/1

Y1 - 2018/4/1

N2 - A tuple of commuting operators (S1, ⋯ , Sn-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.

AB - A tuple of commuting operators (S1, ⋯ , Sn-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.

KW - Canonical decomposition

KW - Spectral set

KW - Symmetrized polydisc

KW - Γ -Contraction

UR - https://www.scopus.com/pages/publications/85028571764

U2 - 10.1007/s11785-017-0721-1

DO - 10.1007/s11785-017-0721-1

M3 - Article

AN - SCOPUS:85028571764

SN - 1661-8254

VL - 12

SP - 931

EP - 943

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

IS - 4

ER -

Canonical Decomposition of Operators Associated with the Symmetrized Polydisc

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this