Journal of Operator Theory

Volume 63, Issue 1, Winter 2010 pp. 101-114.

Reflexivity and hyperreflexivity of the space of locally intertwining operators

Authors: Janko Bracic, Vladimir Mueller (2), and Michal Zajac (3)
Author institution: (1) University of Ljubljana, IMFM, Jadranska ul. 19, SI-1000 Ljubljana, Slovenia
(2) Mathematical Institute, Czech Academy of Sciences, Zitna 25, 115 67 Prague 1, Czech Republic
(3) Department of Mathematics, Slovak University of Technology, SK-812 19 Bratislava, Slovakia

Summary: An operator

$S$ is a local intertwiner of operators

$A$ and

$B$ at vector

$e$ if

$SAe=BSe$ . We characterize the spaces of all local intertwiners

$\Int(A,B;e)$ that are reflexive (hyperreflexive). We show that in all interesting cases the reflexivity (hyperreflexivity) of

$\Int(A,B;e)$ depends only on

$B$ and is independent of

$A$ and

$e$ . This has consequences concerning the reflexivity of the space of intertwiners

$\Int(A,B)$ and of the commutant of an operator.

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