Operator theory 1100-3TO

The course is a continuation of "Functional analysis I". It aims to cover basic concepts of the theory of operators on Hilbert spaces focusing mainly on spectral theory (functional calculus) and some advanced topics.

Syllabus:

1. bounded operators and their spectra, spectral radius, the resolvent,

2. positive operators, projections, partial isometries, polar decomposition,

3. functional calculus,

4. compact, trace class, and Hilbert-Schmidt operators,

5, unbounded operators, the concept of adjoint operator, functional calculus for self-adjoint operators,

6. self-adjoint extensions of symmetric operators,

7. one-parameter groups of operators and their generators.

Student's work load: 70 h includes
Lectures and classes: 60 h
Preparation for the exam: 10 h