We will use the book "Analysis Now" by Gert K. Pedersen. The book is published by Springer-Verlag (we'll use the 2nd revised printing from 1996) and has ISBN 978-0-387-96788-2. The course will cover most of the material in chapters 2, 4 and 5.
St?ttepensum/Additional reading: Parts of chapter 2 in Analysis Now are also covered in chapter 5 of "Linear Functional Analysis" by Rynne, Bryan P., Youngson, Martin, 2nd edition, 2008, Springer Undergraduate Mathematics Series, ISBN: 978-1-84800-004-9. We will refer to Rynne and Youngson for some of the proofs and for exercises.
The required material for the exam consists of the following sections in "Analysis Now": 2.2, 2.3, 2.4 (except 2.4.13), 2.5 (2.5.1-2.5.8), 4.1, 4.2, 4.3, 4.4 (4.4.1-4.4.4), 4.5 (4.5.6-4.5.11; for the proof of 4.5.8 we refer to G. Murphy's book "C*-algebras and operator theory" (Theorem 2.5.5); only the first half of 4.5.10), 5.1 (5.1.1-5.1.9; in 5.1.9 only (i) (except the statement on the core), (ii) and (iii), 5.2 (5.2.1-5.2.6).