Lærebok
Rynne, Bryan P., Youngson, Martin: Linear Functional Analysis, 2nd edition, 2008. Springer Undergraduate Mathematics Series. ISBN: 978-1-84800-004-9.
Pensum
The relevant material for the exam consists of the following chapters from the book by Rynne and Youngson:
Chapter 1, chapter 2, chapter 3, chapter 4 (except the proofs of 4.43, 4.44, 4.45, 4.52 and 4.53), section 5.1, section 5.3 (only 5.19-without proof, 5.21 and 5.22), section 5.5 (only up to 5.41), chapter 6, chapter 7, and, in addition to this, the exercises that have been assigned during the semester. Also, look at all other exercises in the book which are relevant to the theory as listed above.
Anbefalt tilleggslesning/Suggestions for additional reading
Peter D. Lax: Functional Analysis, 2002. Wiley. ISBN: 0-471-55604-1.
Boka til Lax dekker hele pensum i kursene MAT4340 og MAT4350, men går mye lenger i anvendelser. Grunnen til at den ikke brukes som lærebok i kurset er at den inneholder for mye stoff. Den anbefales som tilleggslesning for alle som ønsker å gå videre i emner basert på matematisk analyse.
Lax's book covers the curriculum requirements for the courses MAT4340 and MAT4350, and goes deeper into applications. However, it contains a lot more material than required for these courses. Nevertheless, it is recommended as additional reading for all those who wish to study further topics in analysis.
John Conway, An introduction to Functional Analysis, Springer-Verlag. (Covers more material than the book by Rynne and Youngson, but is still pedestrian.)
Gert K. Pedersen, Analysis Now, Springer-Verlag. (This book covers material on topology, normed spaces and duality, Hilbert spaces, operator algebras, unbounded operators, and a chapter on measure and integration. The style is elegant but condensed, and the material is particularly well organised.)