JournalszaaVol. 13, No. 2pp. 233–260

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, Netherlands
  • S.A.M. Marcantognini

    Universidad Simón Bolívar, Caracas, Venezuela
  • H.S.V. de Snoo

    Rijksuniversiteit Groningen, Netherlands
A Schur Type Analysis of the Minimal Unitary Hubert Space Extensions of a Krein Space Isometry whose Defect Subspaces are Hubert Spaces cover
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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