Open Daily: 10am - 10pm | Alley door pickup 10am - 7pm 3038 Hennepin Ave Minneapolis, MN
612-822-4611

  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Banach Spaces and Descriptive Set Theory: Selected Topics

Banach Spaces and Descriptive Set Theory: Selected Topics

Dodos, Pandelis

Paperback

Series: Lecture Notes in Mathematics, Book 1993

FictionGeneral Mathematics

ISBN10: 3642121527
ISBN13: 9783642121524
Publisher: Springer
Published: May 11 2010
Pages: 168
Weight: 0.58
Height: 0.39 Width: 6.14 Depth: 9.21
Language: English
These notes are devoted to the study of some classical problems in the Geometry of Banach spaces. The novelty lies in the fact that their solution relies heavily on techniques coming from Descriptive Set Theory. Thecentralthemeisuniversalityproblems.Inparticular, thetextprovides an exposition of the methods developed recently in order to treat questions of the following type: (Q) LetC be a class of separable Banach spaces such that every space X in the classC has a certain property, say property (P). When can we ?nd a separable Banach space Y which has property (P) and contains an isomorphic copy of every member ofC? We will consider quite classical properties of Banach spaces, such as - ing re?exive, having separable dual, not containing an isomorphic copy of c, being non-universal, etc. 0 It turns out that a positive answer to problem (Q), for any of the above mentioned properties, is possible if (and essentially only if) the classC is simple. The simplicity ofC is measured in set theoretic terms. Precisely, if the classC is analytic in a natural coding of separable Banach spaces, then we can indeed ?nd a separable space Y which is universal for the class C and satis?es the requirements imposed above.

Also in

General Mathematics

View All