Syllabus :
Tentatively the syllabus consists of the following chapters from the book Linear Functional Analysis, 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. If there is enough time we will also include some applications and examples taken from the first few sections of chapter 8.
Suggestions for additional reading:
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 somewhat condensed, and the material is well organised.)
Walter Rudin, Functional Analysis, McGraw-Hill Book Company. (The approach is rather general and relatively advanced.)
Peter D. Lax: Functional Analysis, 2002. Wiley. ISBN: 0-471-55604-1. Lax's book covers the syllabus requirements for the courses MAT4340 and MAT4350, and goes deeper into applications. The book contains relatively few exercises. However, it contains a lot more material than required for these courses. Lax's book is recommended as additional reading for all those who wishes to study further topics in analysis.