The Commutant Lifting Theorem for Contractions on Kreĭn Spaces

Aad Dijksma,Michael Dritschel,Henk de Snoo,Stefania Marcantognini

doi:10.1007/978-3-0348-8575-1_4

The Commutant Lifting Theorem for Contractions on Kreĭn Spaces

Aad Dijksma, Michael Dritschel + Show 2 more

https://doi.org/10.1007/978-3-0348-8575-1_4

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Publication Date: Jan 1, 1993

Citations: 3

Affiliation: University of Groningen

#Bijective Correspondence #Unitary Space + Show 8 more

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Abstract

A proof of the commutant lifting theorem for contractions on Kreĭn spaces is given. This is done by associating to the data a suitable isometry V so that a solution of the lifting problem is obtained directly from a unitary Hilbert space extension of V. Furthermore, a bijective correspondence between the solutions and the family of all minimal unitary Hilbert space extensions of V is established. In the Hilbert space case the method is due to R. Arocena.

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