Sumários

Exercises on convex sets and Hahn-Banach

23 Outubro 2017, 18:00 • Luís Fernando Sanchez Rodrigues

Exercises on convex sets and Hahn-Banach

Hahn-Banach theorem, continued

23 Outubro 2017, 17:00 • Luís Fernando Sanchez Rodrigues

Hahn-Banach theorem in normed spaces (real or complex).

Minkowski functional. Separation of a convex set and a point by a closed hyperplane.

A problem on the Hahn-banach theorem.

19 Outubro 2017, 17:00 • Luís Fernando Sanchez Rodrigues

A problem on the Hahn-banach theorem.

Some notes about adjoints. Closed ranges. The Hahn-Banach theorem

19 Outubro 2017, 16:00 • Luís Fernando Sanchez Rodrigues

Notes about adjoints: in a complex Hilbert space, sel-adjointness of A is equivalent to Ax.x to be real for all x.

The closure of the range of A is the ortogonal of the kernel of A*.
A condition for the closure of the range of an operator in Banach spaces.
The abstract Hahn Banach theorem.

Discussion of exercises

17 Outubro 2017, 16:30 • Luís Fernando Sanchez Rodrigues

Exercises on the open mapping theorem.