The curriculum for the course is taken from Chapters 1, 2, 3, 4 and 5 in the following book:
G.K. Pedersen: Analysis Now, 1989. Springer. ISBN: 978-0-387-96788-2. Corrected 2nd printing. Link to Springer's homepage for this book.
The detailed teaching plan can be found under "Schedule" on the course homepage. The material relevant for the exam is (referring to section numbering): 1.3, 1.6 (1.6.1, 1.6.2, 1.6.10), 2.1 (except 2.1.15 and 2.1.17 for finite p), 2.4 (except 2.4.12 and 2.4.13), 2.5 (up to and including 2.5.7), 3.2 (up to 3.2.20), 3.3 (up to 3.3.17), 3.4 (up to 3.4.13), 4.1, 4.2 (up to 4.2.6), 4.3, 4.4 (up to 4.4.12), 4.5, 4.6 (up to 4.6.7), 5.1 (up to 5.1.16).
Additional book: Rynne, Bryan P., Youngson, Martin, "Linear Functional Analysis", 2nd edition, 2008, Springer Undergraduate Mathematics Series, ISBN: 978-1-84800-004-9. Chapter 6 on "Linear Operators on Hilbert Spaces".
Occasionally we will refer to the lectures notes by G. Teschl "Topics in Real and Functional Analysis" that have been used in MAT4400 and MAT4410. Link to the current version of the notes may be found on the web-pages of these courses.