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Bounded and unbounded operators on Hilbert spaces
01THTUR
A.A. 2024/25
Course Language
Inglese
Degree programme(s)
Doctorate Research in Scienze Matematiche - Torino
Course structure
| Teaching | Hours |
|---|---|
| Lezioni | 25 |
Lecturers
| Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut | Years teaching |
|---|---|---|---|---|---|---|---|
| Martini Alessio | Professore Ordinario | MATH-03/A | 25 | 0 | 0 | 0 | 1 |
Co-lectures
Context
| SSD | CFU | Activities | Area context |
|---|---|---|---|
| *** N/A *** |
The course aims at presenting some elements of spectral theory for bounded and unbounded operators on Hilbert spaces.
Basic notions (at undergraduate university level) of linear algebra, topology, measure theory and functional analysis.
The following syllabus may be adjusted based on the participants' interests.
1) Review of Hilbert spaces and spectral theory for bounded operators.
2) Commutative C*-algebras and the Gelfand-Naimark theorem.
3) The spectral theorem for bounded normal operators.
4) Unbounded operators: domain, closure, adjoint, symmetry and self-adjointness, spectrum.
5) The spectral theorem for unbounded self-adjoint operators.
6) One-parameter groups of unitary operators and Stone's theorem.
7) Self-adjoint extensions of symmetric operators (deficiency indices, Friedrichs' extension).
On site
Oral presentation
P.D.2-2 - March
The course takes place in March 2025. Schedule: Wednesday 5,12,19 between 10:00-13:00; Thursday 6,13,20 and Friday 7,14,21 between 9:00-12:00.