# On the intertwinings of regular dilations

Annales Polonici Mathematici (1997)

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

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topDumitru 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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