This course studies the central ideas of functional analysis, focussing primarily on normed vector spaces.

Highlights include:

• The Hahn-Banach theorem (in various guises)
• The open mapping and closed graph theorems
• The Banach-Steinhaus theorem
• Dual spaces
• Weak convergence
• Banach-Alaoglus theorem
• Spectral theory for self-adjoint operators

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• Main text: Introductory Functional Analysis with Applications, by Kreyszig. We aim to cover chapters 4, 7, 9.
• Supplementary material: Course notes from 2006

The above notes were written by Professor Hanche-Olsen who taught this course for a stint a few years' ago. They have not been written explicitly for this version of the course but are still highly relevant. As Professor Hanche-Olsen is not the current instructor, comments and corrections should be sent to me; I shall pass them on in one lot at the end of the course.

The schedule is:

• Monday 14:15-16:00, room B21
• Thursday 9:15-11:00, room F6

The first lecture will be on Thursday January 10th.

There will be no lectures in weeks 9 and 10 (except for the revision lecture in week 10).

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The Midterm exam will take place on Friday 7th March between 10am and 12noon in B22.

There will be a revision lecture on Monday 3rd March at the usual time (2:15pm to 4pm) in the usual location (B21).

Solutions

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This course will be taught in English. The course text and supplementary material are also written in English. Professor Hanche-Olsen has a dictionary of common mathematical terms which may be of use to some.

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