Hyponormal Pairs of Commuting Operators

  • Raúl E. Curto
  • Paul S. Muhly
  • Jingbo Xia
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 35)

Abstract

We analyze the notions of weak and strong joint hyponormality for commuting pairs of operators, with an aim at understanding the gap between hyponormality and subnormality for single operators. We exhibit a commuting pair T = (T1, T2) such that:
  1. (i)

    T is weakly hyponormal;

     
  2. (ii)

    T is not strongly hyponormal;

     
  3. (iii)

    T 1 1T 2 2 is subnormal (all ℓ1, ℓ2 ≥ 0);

     
  4. (iv)

    T1 + T2 is not subnormal;

     
  5. (v)

    T1 + T2 is power hyponormal; and

     
  6. (vi)

    T1 is unitarily equivalent to T2.

     

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Copyright information

© Birkhäuser Verlag Basel 1988

Authors and Affiliations

  • Raúl E. Curto
    • 1
  • Paul S. Muhly
    • 1
  • Jingbo Xia
    • 2
  1. 1.Department of MathematicsUniversity of IowaIowa CityUSA
  2. 2.Department of MathematicsSUNY at BuffaloBuffaloUSA

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