Instructor: Florent Baudier
Office: Blocker 525J
Office hours: TR 1:00-2:00 p.m. or by appointment
Lectures: TR 2:20 p.m.-3:35 p.m. BLOC 148
Course description: Normed linear spaces, duality theory, reflexivity, basis theory, structure theory of Banach spaces. Textbooks:

Topics in Banach Space Theory, F. Albiac and N. Kalton

Classical Banach spaces I, Y. Lindenstrauss and L. Tzafriri

A Short Course on Banach Space Theory, N. L. Carothers

An Introduction to Banach Space Theory, R. E. Megginson

Banach Space Theory (The Basis for Linear and Nonlinear Analysis), M. Fabian, P. Habala, P. Hajek, V. Montesinos, V. Zizler

Exams Homework   Schedule

Date of Class	Material covered
Tuesday 08/26	Introduction, Dual pairs
Thursday 08/28	Banach-Alaoglu, weak and weak* topologies
Tuesday 09/02	Hahn-Banach theorem in locally convex topological vector spaces, Goldstine Theorem, Mazur's Theorem
Thurssday 09/04	Eberlein-Smulian Theorem
Tuesday 09/09	Eberlein-Smulian Theorem
Thursday 09/11	Helly's Theorem, Topological and geometric characterization of reflexivity
Tuesday 09/16	Topological and geometric characterization of reflexivity
Thursday 09/18	Local structure of Banach spaces: finite representability, ultrapoducts of Banach spaces
Tuesday 09/23	Local structure of Banach spaces: principle of local reflexivity, bidual of spaces of bounded operators
Thursday 09/25	Local structure of Banach spaces:principle of local reflexivity, bidual of spaces of bounded operators
Tuesday 09/30	Basis theory: Schauder bases, equivalence of bases, basic sequences
Thursday 10/02	Basis theory: Schauder bases, equivalence of bases, basic sequences
Tuesday 10/07	small perturbation principle(s)
Thursday 10/09	block basic sequences
Tuesday 10/14	Fall break
Thursday 10/16	Bessaga-Pelczynski selection principle, subspaces of ℓp
Tuesday 10/21	Shrinking bases
Thursday 10/28	Boundedly complete bases, duality, James' reflexivity theorem
Tuesday 10/28	Unconditionally convergent series in Banach spaces: Orlicz's theorem
Thursday 10/30	Unconditional bases, James' structure theorems
Tuesday 11/04	Khitchine's inequality and application to Hilbertian subspaces of Lp
Thursday 11/06	Orlicz's theorem for unconditionally convergent sequences in Lp 1≤ p≤ 2.
Tuesday 11/11	Class does no meet
Thursday 11/13	Kadec-Pelczynski theorem, dichotomy for subspaces of Lp.
Tuesday 11/18	Banach-Saks theorem, definition and first properties of type and cotype
Thursday 11/20	type and cotype of Lp-spaces, separable Banach spaces as quotients of ℓ1
Tuesday 11/25	class does not meet
Thursday 11/27	Thanksgiving break
Tuesday 12/02	uniform convexity, Milman-Pettis theorem, p-uniformy convexity: definition and examples, connection with cotype
Thursday 12/04	James ℓ1 theorem, Tsirelson space