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On CNC commuting contractive tuples

  • T. BhattacharyyaEmail author
  • J. Eschmeier
  • J. Sarkar
Article

Abstract

The characteristic function has been an important tool for studying completely non-unitary contractions on Hilbert spaces. In this note, we consider completely non-coisometric contractive tuples of commuting operators on a Hilbert space H. We show that the characteristic function, which is now an operator-valued analytic function on the open Euclidean unit ball in ℂn, is a complete unitary invariant for such a tuple. We prove that the characteristic function satisfies a natural transformation law under biholomorphic mappings of the unit ball. We also characterize all operator-valued analytic functions which arise as characteristic functions of pure commuting contractive tuples.

Keywords

Characteristic function invariant subspaces biholomorphic automorphisms functional model coincidence 

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Copyright information

© Indian Academy of Sciences 2006

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.Fachbereich MathematikUniversität des SaarlandesSaarbrückenGermany

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