# Algebras and subspaces of operators ## Past sessions

### Algebras and subspaces of operators: invariant subspaces, reflexivity, hyperreflexivity and transitivity - III

1. Invariant subspaces, examples of lattices of invariant subspaces.
2. Reflexivity, transitivity and hyperreflexivity equivalent definitions for algebras and
3. subspaces.
4. Case of finite dimensional underlying Hilbert space.
5. Finite dimensional subspaces of operators.
6. Case of subspaces and subalgebras of Toeplitz operators on the unit disc.
7. Toeplitz operators on the upper-half plane, simply- and multi-connected regions.
8. Generalized Toeplitz operators.
9. Toeplitz operators on Bergman space.
10. Isometries and quasinormal operators.
11. Consistent operators and power partial isometries.
12. Multioperator case.

The course targets doctoral students and anybody else interested in the subject.

### Algebras and subspaces of operators: invariant subspaces, reflexivity, hyperreflexivity and transitivity - II

1. Invariant subspaces, examples of lattices of invariant subspaces.
2. Reflexivity, transitivity and hyperreflexivity equivalent definitions for algebras and
3. subspaces.
4. Case of finite dimensional underlying Hilbert space.
5. Finite dimensional subspaces of operators.
6. Case of subspaces and subalgebras of Toeplitz operators on the unit disc.
7. Toeplitz operators on the upper-half plane, simply- and multi-connected regions.
8. Generalized Toeplitz operators.
9. Toeplitz operators on Bergman space.
10. Isometries and quasinormal operators.
11. Consistent operators and power partial isometries.
12. Multioperator case.

The course targets doctoral students and anybody else interested in the subject.

### Algebras and subspaces of operators: invariant subspaces, reflexivity, hyperreflexivity and transitivity - I

1. Invariant subspaces, examples of lattices of invariant subspaces.
2. Reflexivity, transitivity and hyperreflexivity equivalent definitions for algebras and
3. subspaces.
4. Case of finite dimensional underlying Hilbert space.
5. Finite dimensional subspaces of operators.
6. Case of subspaces and subalgebras of Toeplitz operators on the unit disc.
7. Toeplitz operators on the upper-half plane, simply- and multi-connected regions.
8. Generalized Toeplitz operators.
9. Toeplitz operators on Bergman space.
10. Isometries and quasinormal operators.
11. Consistent operators and power partial isometries.
12. Multioperator case.

The course targets doctoral students and anybody else interested in the subject.

Partially supported by project PTDC/MAT/121837/2010 (FCT/Portugal). 