Banach spaces and Ramsey theory, Spring 2007
Instructor: Christian Rosendal, room 304 Altgeld Hall
Course hours: Tuesday and Thursday 9:00 - 10:20 AM in Altgeld Hall 141.
Classes begin 12-Mar-07 and end 02-May-07.
This is a half semester course on the geometry of Banach spaces with a heavy emphasis on the applications of combinatorial, model-theoretical, and descriptive set theoretical methods.
The goal is to introduce the fundamental notions about Schauder bases, which are the natural generalisation of vector-space bases to the infinite dimension, and then rapidly go on to prove some of the deep results of the subject.
An overview:
Notes:
There is no required reading, but several excellent textbooks are available.
Graduate Texts in Mathematics, 233. Springer, New York, 2006. xii+373 pp.
CMS Books in Mathematics/Ouvrages de Mathematiques de la SMC, 8. Springer-Verlag, New York, 2001. x+451 pp.
Graduate Texts in Mathematics, 92. Springer-Verlag, New York, 1984. xii+261 pp.
Advanced Courses in Mathematics. CRM Barcelona. Birkhäuser Verlag, Basel, 2005. viii+257 pp.
Cours Specialises, 12. Societe Mathematique de France, Paris, 2004. xxiv+627 pp.
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