バナッハ空間と記述的集合論 Banach Spaces and Descriptive Set Theory: Selected Topics (Lecture Notes in Mathematics 1993) 〈Vol. 1993〉

Dodos, Pandelis

Springer（2010発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 160 p.
• 言語 ENG
• 商品コード 9783642121524

Full Description

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.

Contents

Basic Concepts.- The Standard Borel Space of All Separable Banach Spaces.- The ?2 Baire Sum.- Amalgamated Spaces.- Zippin's Embedding Theorem.- The Bourgain-Pisier Construction.- Strongly Bounded Classes of Banach Spaces.