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

Aad Dijksma | Zendy; Stefania Marcantognini | Zendy; H. S. V. de Snoo | Zendy

Open Access

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

Author(s) -

Aad Dijksma,

Stefania Marcantognini,

H. S. V. de Snoo

Publication year - 1994

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/513

Subject(s) - linear subspace , isometry (riemannian geometry) , unitary state , space (punctuation) , pure mathematics , type (biology) , mathematics , algebra over a field , computer science , ecology , political science , law , biology , operating system

We consider a Kreln 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 Kreln space contractions.

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