Functional Analysis I

5 credits

Syllabus, Master's level, 1MA043

This course has been discontinued.

A revised version of the syllabus is available.

Code: 1MA043
Education cycle: Second cycle
Main field(s) of study and in-depth level: Mathematics A1N
Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by: The Faculty Board of Science and Technology, 24 April 2008
Responsible department: Department of Mathematics

Entry requirements

120 credit points with 50 credit points Mathematics including Linear Algebra II and Transform Methods

Learning outcomes

In order to pass the course (grade 3) the student should be able to

use basic functional analytic formalism in normed spaces;

use ON-systems and orthogonal projections in Hilbert spaces;

solve simple problems about the weak topology;

solve simple Hilbert space spectral theory problems.

Content

Topology in metric spaces. Normed spaces. Banach spaces, inner product spaces, Hilbert spaces. Linear maps. Basic functional analytic theorems: Hahn–Banach's theorem, Banach–Steinhaus' theorem, the open map and the closed graph theorems. Weak convergence. Operators on Hilbert spaces. Geometry in Hilbert spaces. The spectral theory for compact symmetric operators.

Instruction

Lectures and problem solving sessions.

Assessment

Written and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.