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We study operators whose commutant is reflexive but not hyperreflexive. We construct a C₀ contraction and a Jordan block operator associated with a Blaschke product B which have the above mentioned property. A sufficient condition for hyperreflexivity of is given. Some other results related to hyperreflexivity of spaces of operators that could be interesting in themselves are proved.
Roman V. Bessonov, Janko Bračič, and Michal Zajac. "Non-hyperreflexive reflexive spaces of operators." Studia Mathematica 202.1 (2011): 65-80. <http://eudml.org/doc/285639>.
@article{RomanV2011, abstract = {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.}, author = {Roman V. Bessonov, Janko Bračič, Michal Zajac}, journal = {Studia Mathematica}, keywords = {reflexive and hyperreflexive subspaces; hyperreflexivity constant; -contractions; Blaschke products}, language = {eng}, number = {1}, pages = {65-80}, title = {Non-hyperreflexive reflexive spaces of operators}, url = {http://eudml.org/doc/285639}, volume = {202}, year = {2011}, }
TY - JOUR AU - Roman V. Bessonov AU - Janko Bračič AU - Michal Zajac TI - Non-hyperreflexive reflexive spaces of operators JO - Studia Mathematica PY - 2011 VL - 202 IS - 1 SP - 65 EP - 80 AB - 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. LA - eng KW - reflexive and hyperreflexive subspaces; hyperreflexivity constant; -contractions; Blaschke products UR - http://eudml.org/doc/285639 ER -