Functional Models and Minimal Contractive Liftings

Santanu Dey, Rolf Gohm, Kalpesh Haria

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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.
Original languageEnglish
Pages (from-to)933-955
Number of pages23
JournalComplex Analysis and Operator Theory
Issue number4
Early online date20 Jul 2014
Publication statusPublished - 20 Jul 2014


  • Characteristic function
  • minimal contractive lifting
  • row contraction
  • multi-analytic
  • completely non-coisometric
  • schur function


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