|
|
|
back 
|
|
On the reflexivity, hyperreflexivity and transitivity of algebras
and subspaces of operators
|
The recent reflexivity, transitivity and hyperreflexivity results for
subspaces and algebras of operators will be presented. We start with
the situation when underlying Hilbert space is finite
dimensional
and giving some examples show that even in this case the notion of
reflexivity is interesting. It will be presented that reflexivity and
hypereflexivity are equivalent for finite dimensional subspaces of
operators even the underlying Hilbert space is not finite dimensional
(positive answer for Larson--Kraus problem). We will study the
dichotomic behavior (reflexivity versus transitivity) of subspaces of
Toeplitz operators on the Hardy space. The Toeplitz operators on the
Bergman space
will be also considered. We discuss also algebras
generated by isometries, power partial isometries and quasinormal
operators. The multivariable case will be also presented. |
back |
|
|