Canonical decomposition of a tetrablock contraction and operator model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:438

Article

Pal, Sourav¹ 

[1] Indian Inst Technol, Dept Math, Bombay 400076, Maharashtra, India

关键词: Tetrablock contraction;    Canonical decomposition;    Fundamental operators;    Operator model;   

DOI  :  10.1016/j.jmaa.2016.02.027

来源: Elsevier

【 摘 要 】

A triple of commuting operators for which the closed tetrablock (E) over bar is a spectral set is called a tetrablock contraction or an E-contraction. The set E is defined as E = {(x(1), x(2), x(3)) is an element of C-3 : 1 - zx(1) - wx(2) + zwx(3) not equal 0 whenever vertical bar z vertical bar <= 1, vertical bar w vertical bar <= 1}. We show that every IE-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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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