A Schur Type Analysis of the Minimal Unitary Hubert Space Extensions of a Krein Space Isometry whose Defect Subspaces are Hubert Spaces
Aad Dijksma
Rijksuniversiteit Groningen, NetherlandsS.A.M. Marcantognini
Universidad Simón Bolívar, Caracas, VenezuelaH.S.V. de Snoo
Rijksuniversiteit Groningen, Netherlands
Abstract
We consider a Krein space isometry whose defect subspaces are Hilbert spaces and we show that its minimal unitary Hilbert space extensions are related to one-step isometric Hilbert space extensions and Schur parameters. These unitary extensions give rise to moments and scattering matrices defined on a scale subspace. By means of these notions we solve the labeling problem for the contractive intertwining liftings in the commutant lifting theorem for Krein space contractions.
Cite this article
Aad Dijksma, S.A.M. Marcantognini, H.S.V. de Snoo, A Schur Type Analysis of the Minimal Unitary Hubert Space Extensions of a Krein Space Isometry whose Defect Subspaces are Hubert Spaces. Z. Anal. Anwend. 13 (1994), no. 2, pp. 233–260
DOI 10.4171/ZAA/513