Banach spaces and descriptive set theory: selected topics / Pandelis Dodos

Auteur: Dodos, Pandelis (1974-) - AuteurType de document: MonographieCollection: Lecture notes in mathematics ; 1993Langue: anglaisPays: AllemagneÉditeur: Berlin : Springer, cop. 2010Description: 1 vol. (XI-161 p.) ; 24 cm ISBN: 9783642121524 ; br. Résumé: This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous “intermediate” results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective. (Source : Springer).Bibliographie: Bibliogr. p. 155-157. Index. Sujets MSC: 46B03 Functional analysis -- Normed linear spaces and Banach spaces; Banach lattices -- Isomorphic theory (including renorming) of Banach spaces
46B07 Functional analysis -- Normed linear spaces and Banach spaces; Banach lattices -- Local theory of Banach spaces
46B15 Functional analysis -- Normed linear spaces and Banach spaces; Banach lattices -- Summability and bases
05D10 Combinatorics -- Extremal combinatorics -- Ramsey theory
03E15 Mathematical logic and foundations -- Set theory -- Descriptive set theory
54H05 General topology -- Connections with other structures, applications -- Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
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Bibliogr. p. 155-157. Index

This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous “intermediate” results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective. (Source : Springer)

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