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      https://www.ias.ac.in/article/fulltext/pmsc/116/02/0193-0220

    • Keywords

       

      Dilation; commuting tuples; complete positivity; Cuntz algebras; Cuntz-Krieger algebras

    • Abstract

       

      Given a contractive tuple of Hilbert space operators satisfying certainA-relations we show that there exists a unique minimal dilation to generators of Cuntz-Krieger algebras or its extension by compact operators. This Cuntz-Krieger dilation can be obtained from the classical minimal isometric dilation as a certain maximalA-relation piece. We define a maximal piece more generally for a finite set of polynomials inn noncommuting variables. We classify all representations of Cuntz-Krieger algebrasOA obtained from dilations of commuting tuples satisfyingA-relations. The universal properties of the minimal Cuntz-Krieger dilation and the WOT-closed algebra generated by it is studied in terms of invariant subspaces.

    • Author Affiliations

       

      B V Rajarama Bhat1 Santanu Dey2 Joachim Zacharias3

      1. Indian Statistical Institute, R.V. College Post, Bangalore - 560 059, India
      2. Institut fur Mathematik und Informatik, Ernst-Moritz-Arndt-UniversitÄt, Friedrich-Ludwig-Jahn-Str. 15a, Greifswald - 17487, Germany
      3. School of Mathematical Sciences, University of Nottingham, Nottingham - NG7 2RD, UK
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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