TMA4230 Functional analysis 2004

Lecturer:

Harald HancheOlsen

Literature:

Erwin Kreyszig: Introductory functional analysis with applications, ISBN 0471504599.

Note on transfinite induction (not required reading)

Note on sequence spaces and L^{p} spaces

Note on point set topology

Note on topological vector spaces

Note on spectral theory. A supplement to Kreyszig chapters 7 and 9.

What has been covered in the class:

First, all of the above notes. However, you are not required to have learned anything from the one on transfinite induction. (But you are expected to know about Zorn's lemma.)

Second, Kryszig's book: Chapters 4, 7 and 9, with the exception of sections 4.4, 4.10, 4.11, 7.5.

You will have noticed that there is quite a bit of overlap between my notes and Kreyszig's book. They are too many to enumerate here (I would surely forget some). In those cases, it's OK to read my notes and just skim through the corresponding bits of Kreyszig. In particular, this applies to Kreyszig's sections 9.3 and 9.4.

Exercises

Solution set 1 (pdf/ps) for problems 4.2: 3, 4, 5, 10, and 4.3: 3, 11.

Solution set 2 (pdf/ps) for problems 4.5: 5, 8, 9, 10, and 4.6: 3.

Solution set 3 (pdf/ps) for problems 4.6: 8, 9; 4.7: 5, 6, 7, 8; plus the extra problem (with hint): Prove that a closed subspace of a reflexive space is reflexive.

Solution set 4 (pdf/ps) for problems 4.12: 2, 5, 6, 8; 4.13: 7, 11, 12, 13.

Solution set 5 (pdf/ps) for problem set A, for topology (pdf/ps)

Solution set 6 (pdf/ps) for the review problems 4.3: 7, 14, 15; 4.7: 10, 13, 14; 4.12: 10; plus problem set B (pdf/ps).

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