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Functional Models and Minimal Contractive Liftings

DSpace at IIT Bombay

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Title Functional Models and Minimal Contractive Liftings
 
Creator DEY, S
GOHM, R
HARIA, KJ
 
Subject NONCOMMUTING OPERATORS
INFINITE SEQUENCES
Characteristic function
Minimal contractive lifting
Row contraction
Multi-analytic
Completely non-coisometric
Schur function
 
Description 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 Szego 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.
 
Publisher SPRINGER BASEL AG
 
Date 2016-01-14T12:27:39Z
2016-01-14T12:27:39Z
2015
 
Type Article
 
Identifier COMPLEX ANALYSIS AND OPERATOR THEORY, 9(4)933-955
1661-8254
1661-8262
http://dx.doi.org/10.1007/s11785-014-0399-6
http://dspace.library.iitb.ac.in/jspui/handle/100/17496
 
Language en