| Tid | Lokal | Rubriker | Avsnitt i bok: A. Friedman |
| 12/2 | 3721 | Preliminaries. Metric spaces.
Lebesgue integration |
pages: 90--105, 1--61, 78--89. |
| 26/2 | 3721 | Banach spaces. Bounded operators.
A fixed point theorem. |
pages: 90--105, 123--138.
118--121. |
| 4/3 | 3721 | Hilbert spaces. The Riesz lemma. | pages: 201--212.
Home assignment 1. |
| 11/3 | 3721 | Orthonormal sets in a Hilbert space.
Baire category theorem. Uniform boundedness theorem. |
pages: 213--218, 105--107,
139--141. |
| 18/3 | 3721 | Closed graph theorem. Open mapping theorem.
Bounded inverse theorem. |
one
question
pages: 141--145. Home assignment 2. |
| 25/3 | 3721 | l^p spaces and L^p spaces. The spaces C[a,b] and c_0. | pages: 92--105.
(handouts for L^p) |
| 15/4 | 3721 | Definition of a dual space. Dual to L^p and C[a,b].
Formulation of the Hahn-Banach theorem |
pages: 150--155,
159--164, 176--185. |
| 29/4 | 3721 | Weak topologies. The Banach-Alaoglu theorem. | pages: 168--171. |
| 6/5 | 3721 | The adjoint operator. | pages: 172--175, 209--212. Home assignment 3. |
| 13/5 | 3721 | Basic concepts of the spectral theory.
Spectral properties of bounded operators. Spectral radius. |
pages: 218--237. |
| 19/5 OBS! | 3721 | Definition of a compact operator.
Spectral properties of compact operators. |
pages: 186--189, 194--197. |
| 27/5 | 3721 | Spectral properties of compact operators.
The Fredholm alternative. |
pages: 194--197, 189--194. |