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Non-hyperreflexive reflexive spaces of operators

Roman V. Bessonov; Janko Bračič; Michal Zajac — 2011

Studia Mathematica

We study operators whose commutant is reflexive but not hyperreflexive. We construct a C₀ 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.

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