• On subnormal operators

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/095/01/0041-0044

    • Keywords

       

      Subnormal operators; self-dual subnormal operators; quasinormal operators; unilateral shifts; C*-algebra; C*-spectral inclusion property

    • Abstract

       

      LetS be a pure subnormal operator such thatC*(S), theC*-algebra generated byS, is generated by a unilateral shiftU of multiplicity 1. We obtain conditions under which 5 is unitarily equivalent toα + βU, α andβ being scalars orS hasC*-spectral inclusion property. It is also proved that if in addition,S hasC*-spectral inclusion property, then so does its dualT andC*(T) is generated by a unilateral shift of multiplicity 1. Finally, a characterization of quasinormal operators among pure subnormal operators is obtained.

    • Author Affiliations

       

      B C Gupta1

      1. Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar - 388 120, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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