On the intertwinings of regular dilations

• Autorzy: Dumitru Gaşpar , Nicolae Suciu
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 47A13: Several-variable operator theory (spectral, Fredholm, etc.)
• 47A20: Dilations, extensions, compressions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 66
• Numer: 1
• Strony: 105-121

Daty

wydano

1997

otrzymano

1995-07-12

poprawiono

1996-01-08

Twórcy

autor

Dumitru Gaşpar

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

autor

Nicolae Suciu

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

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