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      https://www.ias.ac.in/article/fulltext/pmsc/116/03/0299-0316

    • Keywords

       

      Characteristic function; invariant subspaces; biholomorphic automorphisms; functional model; coincidence

    • 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.

    • Author Affiliations

       

      T Bhattacharyya1 J Eschmeier2 J Sarkar1

      1. Department of Mathematics, Indian Institute of Science, Bangalore - 560 012, India
      2. Fachbereich Mathematik, Universität des Saarlandes, Saarbrücken - 66123, Germany
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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