Daniel Ueltschi

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2007-2008, Term 2 (Winter)

MA3G8 - Functional Analysis II

***SPECIAL SESSION*** Tuesday 20 May, 11:00 - 12:30, Room B1.01 (Zeeman building)
Questions can be emailed in advance, in order to get clearer answers!

Here is the official site from the department.

Time and place: Thu 1-2 in MS.04; Fri 2-4 in MS.05. Supervision Tue 10-11 in B3.01, by Patrick O'Callaghan.

Assessment: 3-hour examination.

Description:

Many problems in Mathematics lead to linear problems in infinite-dimensional spaces. In this course we shall mainly study infinite-dimensional normed linear spaces and continuous linear transformations between such spaces. We will study Banach spaces and prove the main theorems of this subject (Hahn-Banach, open mapping, uniform boundedness). The last part of the course will be devoted to bounded and unbounded operators, with specific mention of differential operators in L2 spaces.
Here is the table of contents.

Errata:

Gareth Speight pointed out an omission in Theorem 3.5 (Uniform boundedness). We suppose in addition that all operators T_n are bounded.

Assignments:

assignment 1	(10.01.08)
assignment 2	(17.01.08)
assignment 3	(24.01.08)
assignment 4	(31.01.08)
assignment 5	(07.02.08)
assignment 6	(14.02.08)
assignment 7	(22.02.08)	solution
assignment 8	(28.02.08)
assignment 9	(08.03.08)

References:

E. Kreyszig, Introductory Functional Analysis with Applications, Wiley, 1989.
W. Rudin, Functional Analysis, McGraw-Hill, 1973.
G.B. Folland, Real Analysis, Wiley, 1999.
J.K Hunter and B. Nachtergaele, Applied Analysis, World Scientific, 2001.
Also, Clement Tsang's Note on nowhere dense sets