✦ LIBER ✦
Transference of Metrics Induced by Unitary Couplings, a Sarason Theorem for the Bidimensional Torus, and a Sz.-Nagy-Foias Theorem for Two Pairs of Dilations
✍ Scribed by M. Cotlar; C. Sadosky
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 489 KB
- Volume
- 111
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
Liftings of invariant forms defined in semi-invariant subspaces of the Hilbert spaces of scattering systems with one or two evolution groups are obtained. These liftings provide direct proofs for the classical theorems of Sarason and of Sz.-Nagy and Foias, as well as a bidimensional version of Sarason's theorem, and a theorem of Sz.-Nagy-Foias type for two pairs of dilations. The main tool used is a transference of a Hilbert space metric induced by a coupling of isometries, of possible independent interest in the study of scattering systems. 1993 Academic Press, Inc.