Canonical decomposition of a tetrablock contraction and operator model

Sourav Pal

doi:10.1016/j.jmaa.2016.02.027

Canonical decomposition of a tetrablock contraction and operator model

Sourav Pal

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

7 Scopus citations

Abstract

A triple of commuting operators for which the closed tetrablock E is a spectral set is called a tetrablock contraction or an E-contraction. The set E is defined as. E={(x₁,x₂,x₃)∈C³:1-zx₁-wx₂+zwx₃≠0 whenever |z|≤1,|w|≤1}. We show that every E-contraction can be uniquely written as a direct sum of an E-unitary and a completely non-unitary E-contraction. It is analogous to the canonical decomposition of a contraction operator into a unitary and a completely non-unitary contraction. We produce a concrete operator model for such a triple satisfying some conditions.

Original language	English
Pages (from-to)	274-284
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	438
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2016.02.027
State	Published - 1 Jun 2016
Externally published	Yes

Keywords

Canonical decomposition
Fundamental operators
Operator model
Tetrablock contraction

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2016.02.027

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abstract = "A triple of commuting operators for which the closed tetrablock E is a spectral set is called a tetrablock contraction or an E-contraction. The set E is defined as. E=\{(x1,x2,x3)∈C3:1-zx1-wx2+zwx3≠0 whenever |z|≤1,|w|≤1\}. We show that every E-contraction can be uniquely written as a direct sum of an E-unitary and a completely non-unitary E-contraction. It is analogous to the canonical decomposition of a contraction operator into a unitary and a completely non-unitary contraction. We produce a concrete operator model for such a triple satisfying some conditions.",

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N2 - A triple of commuting operators for which the closed tetrablock E is a spectral set is called a tetrablock contraction or an E-contraction. The set E is defined as. E={(x1,x2,x3)∈C3:1-zx1-wx2+zwx3≠0 whenever |z|≤1,|w|≤1}. We show that every E-contraction can be uniquely written as a direct sum of an E-unitary and a completely non-unitary E-contraction. It is analogous to the canonical decomposition of a contraction operator into a unitary and a completely non-unitary contraction. We produce a concrete operator model for such a triple satisfying some conditions.

AB - A triple of commuting operators for which the closed tetrablock E is a spectral set is called a tetrablock contraction or an E-contraction. The set E is defined as. E={(x1,x2,x3)∈C3:1-zx1-wx2+zwx3≠0 whenever |z|≤1,|w|≤1}. We show that every E-contraction can be uniquely written as a direct sum of an E-unitary and a completely non-unitary E-contraction. It is analogous to the canonical decomposition of a contraction operator into a unitary and a completely non-unitary contraction. We produce a concrete operator model for such a triple satisfying some conditions.

KW - Canonical decomposition

KW - Fundamental operators

KW - Operator model

KW - Tetrablock contraction

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SN - 0022-247X

VL - 438

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EP - 284

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Canonical decomposition of a tetrablock contraction and operator model

Abstract

Keywords

ASJC Scopus subject areas

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