Functional Models and Minimal Contractive Liftings

Autor:	Dey, Santanu, Gohm, Rolf, Haria, Kalpesh J.
Rok vydání:	2014
Předmět:	Mathematics - Operator Algebras Mathematics - Functional Analysis 47A20 47A13 47A15 46L53 46L05
Druh dokumentu:	Working Paper
Popis:	Based on a careful analysis of functional models for contractive multi-analytic operators we establish a one-to-one correspondence between unitary equivalence classes of minimal contractive liftings of a row contraction and injective symbols of contractive multi-analytic operators. This allows an effective construction and classification of all such liftings with given defects. Popescu's theory of characteristic functions of completely non-coisometric row contractions is obtained as a special case satisfying a Szeg\"{o} condition. In another special case of single contractions and defects equal to $1$ all non-zero Schur functions on the unit disk appear in the classification. It is also shown that the process of constructing liftings iteratively reflects itself in a factorization of the corresponding symbols. Comment: 25 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1402.4220 Zobrazit plný text záznamu View this record from Arxiv