On the intertwinings of regular dilations

Dumitru Gaşpar; Nicolae Suciu

Annales Polonici Mathematici (1997)

  • Volume: 66, Issue: 1, page 105-121
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Dumitru Gaşpar, and Nicolae Suciu. "On the intertwinings of regular dilations." Annales Polonici Mathematici 66.1 (1997): 105-121. <http://eudml.org/doc/269938>.

@article{DumitruGaşpar1997,
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.},
author = {Dumitru Gaşpar, Nicolae Suciu},
journal = {Annales Polonici Mathematici},
keywords = {commuting multioperator; *-regular dilation; contractive intertwining; (semi-)subnormal pair; commutant lifting theorem for commuting pairs of contractions; bicontractions; -)regular dilations; contractive intertwinings; semi-subnormal bicontractions},
language = {eng},
number = {1},
pages = {105-121},
title = {On the intertwinings of regular dilations},
url = {http://eudml.org/doc/269938},
volume = {66},
year = {1997},
}

TY - JOUR
AU - Dumitru Gaşpar
AU - Nicolae Suciu
TI - On the intertwinings of regular dilations
JO - Annales Polonici Mathematici
PY - 1997
VL - 66
IS - 1
SP - 105
EP - 121
AB - 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.
LA - eng
KW - commuting multioperator; *-regular dilation; contractive intertwining; (semi-)subnormal pair; commutant lifting theorem for commuting pairs of contractions; bicontractions; -)regular dilations; contractive intertwinings; semi-subnormal bicontractions
UR - http://eudml.org/doc/269938
ER -

References

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  15. [15] S. Parrott, Unitary dilations for commuting contractions, Pacific J. Math. 34 (1970), 481-490. Zbl0202.41802
  16. [16] M. Słociński, Isometric dilations of doubly commuting contractions and related models, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (12) (1977), 1233-1242. Zbl0384.47005
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