The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (1440 KB) | Metadata | Table of Contents | ZAA summary
Volume 13, Issue 2, 1994, pp. 233–260
DOI: 10.4171/ZAA/513

Published online: 1994-06-30

A Schur Type Analysis of the Minimal Unitary Hubert Space Extensions of a Krein Space Isometry whose Defect Subspaces are Hubert Spaces

Aad Dijksma[1], S.A.M. Marcantognini[2] and H.S.V. de Snoo[3]

(1) Rijksuniversiteit Groningen, Netherlands
(2) Universidad Simón Bolívar, Caracas, Venezuela
(3) Rijksuniversiteit Groningen, Netherlands

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.

Keywords: Isometrics, unitary extensions, Krein spaces, Schur parameters, commutant lifting

Dijksma Aad, Marcantognini S.A.M., de Snoo H.S.V.: 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), 233-260. doi: 10.4171/ZAA/513