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Handouts

Chapter 1
Chapter 2 [Omitted material: The definition and examples of separable spaces (page 14) are included and are examinable. The remainder of the section "Separable Hilbert Spaces" (pages 14-17) is omitted and is not examinable.]
Chapter 3
Proof of Proposition 3.2 (now incorporated into Chapter 3 notes)
Chapter 4 [Omitted material: The section "Spectra of Operators on Hilbert Spaces" (pages 10-12 in latest version of notes) is omitted and is not examinable.]
Extra material for MATH41001/MATH61001
Here is a scan of some handwritten notes proving that continuity implies uniform continuity for functions on a compact metric space.

Example Sheet 1 and solutions
Example Sheet 2 and solutions
Example Sheet 3 and solutions [Revised solutions posted on 16/11/09: some missing exponents added in early questions and some more detail for number 6.]
Example Sheet 4 and solutions
Example Sheet 5 and solutions
Example Sheet 6 and solutions [Originally posted 14/12/09 with gap in solution of question 3. Corrected 15/12/09.]
Example Sheet 7 and solutions

Here is a document to help focus your revision by highlighting key topics.

B.P. Rynne and M.A. Youngson, Linear Functional Analysis, Springer (SUMS Series), 2008.
I.J. Maddox, Elements of Functional Analysis, C.U.P. 1989.
G. F. Simmons, An Introduction to Topology and Modern Analysis, McGraw Hill, 1963.