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ArticleOriginal scientific text

Title

On the intertwinings of regular dilations

Authors 1, 1

Affiliations

  1. Department of Mathematics, University of Timişoara, Bv. V. Pârvan 4, 1900 Timişoara, Romania

Abstract

The aim of this paper is to find conditions that assure the existence of the commutant lifting theorem for commuting pairs of contractions (briefly, bicontractions) having (*-)regular dilations. It is known that in such generality, a commutant lifting theorem fails to be true. A positive answer is given for contractive intertwinings which doubly intertwine one of the components. We also show that it is possible to drop the doubly intertwining property for one of the components in some special cases, for instance for semi-subnormal bicontractions. As an application, a result regarding the existence of a unitary (isometric) dilation for three commuting contractions is obtained.

Keywords

ENG
commuting multioperator, *-regular dilation, contractive intertwining, (semi-)subnormal pair

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Annales Polonici Mathematici
1997/66/1
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Pages:
105-121
Main language of publication
English
Received
1995-07-12
Accepted
1996-01-08
Published
1997
Exact and natural sciences