Banach spaces. Bounded operators. Compactness in metric spaces. The Banach-Steinhaus' theorem. The open mapping theorem. The closed graph theorem. Dual spaces. The Hahn-Banach theorem. Dual spaces to Lp and C[0,1]. Weak topologies. The Banach-Alaoglu theorem. Adjoint operators. Campact operators and the Fredholm alternative. Hilbert spaces and operators on Hilbert spaces. The spectral theorem for self-adjoint operators on Hilbert spaces.
SF2707 Functional Analysis 7.5 credits
This course has been discontinued.
Last planned examination: Autumn 2018
Decision to discontinue this course:
No information inserted
Information per course offering
Course offerings are missing for current or upcoming semesters.
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus SF2707 (Autumn 2007–)Headings with content from the Course syllabus SF2707 (Autumn 2007–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
Intended learning outcomes
To give an introduction to the basic concepts and fundamental theorems in functional analysis and operator theory.
Literature and preparations
Specific prerequisites
No information inserted
Literature
Announced at the start of the course- Last time Friedman: Foundations of Modern Analysis, Dover 1982, was used.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
A, B, C, D, E, FX, F
Examination
- TEN1 - Examination, 7.5 credits, grading scale: A, B, C, D, E, FX, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Examiner
No information inserted
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course room in Canvas
Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.
Offered by
Main field of study
Mathematics
Education cycle
Second cycle