Week Dates Subjects References Exercises More
1 11.1 12.1 Linear and normed spaces. Zorns Lemma. Existence of a Hamel basis. Semi norms and quotient spaces. 2-17, 50-67, 210-213. Exercise-1 Selected solutions-1
2 18.1 19.1Basic topology. Banach spaces. Completion theorem. 17-48, 67-72.Exercise-2Basic definitions in topologySelected solutions-2
3 25.1 26.1Category theorem. Bounded linear operators. The spaces B(X,Y). Open mapping theorem (part 1). 246-249, 82-103, 117-119, 285-287.Exercise-3Selected solutions-3
4 1.2 2.2 Open mapping theorem (part 2). Closed operators. Closed graph theorem. Uniform boundedness theorem. 285-297, 249-255Exercise-4None
5 8.2 9.2 Linear functionals. The dual space. Hahn Banach theorem (part 1) 103-111, 120-125, 213-218Exercise-5None
6 15.2 16.2Hahn Banach theorem (part 2). Reflexive spaces.218-224, 239-246Exercise-6None
7 22.2 23.2The dual operator. Systems in separable Banach spaces.231-239Exercise-7None
2010-02-28, hahamov