Frank Plumpton Ramsey.
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.
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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