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.
Tentatively, the required material for the exam consists of the following sections in "Analysis Now" (adjustments of this may occur) : 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; as an alternative a proof of 4.5.8 can also be found in G. Murphy's book "C*-algebras and operator theory" (Theorem 2.5.5) ), 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).