Non-hyperreflexive reflexive spaces of operators

Volume 202 / 2011

Roman V. Bessonov, Janko Bračič, Michal Zajac Studia Mathematica 202 (2011), 65-80 MSC: Primary 47A15; Secondary 47A45, 47L05. DOI: 10.4064/sm202-1-4

Abstract

We study operators whose commutant is reflexive but not hyperreflexive. We construct a $C_0$ contraction and a Jordan block operator $S_B$ associated with a Blaschke product $B$ which have the above mentioned property. A sufficient condition for hyperreflexivity of $S_B$ is given. Some other results related to hyperreflexivity of spaces of operators that could be interesting in themselves are proved.

Authors

  • Roman V. BessonovSteklov Institute of Mathematics
    of Russian Academy of Sciences
    St. Petersburg Department
    e-mail
  • Janko BračičIMFM
    University of Ljubljana
    Jadranska 19
    1000 Ljubljana, Slovenia
    e-mail
  • Michal ZajacDepartment of Mathematics
    Slovak University of Technology
    SK-812 19 Bratislava, Slovakia
    e-mail

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