Unitary N-dilations for tuples of commuting matrices

John E. McCarthy; Orr Moshe Shalit

doi:10.1090/S0002-9939-2012-11714-9

Unitary N-dilations for tuples of commuting matrices

John E. McCarthy, Orr Moshe Shalit

Department of Mathematics

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

11 Scopus citations

Abstract

We show that whenever a contractive k-tuple T on a finite dimensional space H has a unitary dilation, then for any fixed degree N there is a unitary k-tuple U on a finite dimensional space so that q(T) = P_Hq(U)|_H for all polynomials q of degree at most N.

Original language	English
Pages (from-to)	563-571
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	141
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-2012-11714-9
State	Published - 1 Jan 2013

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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title = "Unitary N-dilations for tuples of commuting matrices",

abstract = "We show that whenever a contractive k-tuple T on a finite dimensional space H has a unitary dilation, then for any fixed degree N there is a unitary k-tuple U on a finite dimensional space so that q(T) = PHq(U)|H for all polynomials q of degree at most N.",

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AB - We show that whenever a contractive k-tuple T on a finite dimensional space H has a unitary dilation, then for any fixed degree N there is a unitary k-tuple U on a finite dimensional space so that q(T) = PHq(U)|H for all polynomials q of degree at most N.

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Unitary N-dilations for tuples of commuting matrices

Abstract

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