Non-hyperreflexive reflexive spaces of operators
Volume 202 / 2011
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.
