Banach Spaces and Descriptive Set Theory: Selected Topics: Selected Topics (Lecture Notes in Mathematics): 1993 - Tapa blanda

Dodos, Pandelis

9783642121524: Banach Spaces and Descriptive Set Theory: Selected Topics: Selected Topics (Lecture Notes in Mathematics): 1993

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ISBN 10: 3642121527 ISBN 13: 9783642121524

Editorial: Springer, 2010

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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.

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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.

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ISBN 10 3642121527
ISBN 13 9783642121524
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9783642121548: Banach Spaces and Descriptive Set Theory: Selected Topics

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Banach Spaces and Descriptive Set Theory: Selected Topics

Pandelis Dodos

Publicado por Berlin Springer Berlin Heidelberg Springer Mai 2010, 2010

ISBN 10: 3642121527 ISBN 13: 9783642121524

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Taschenbuch. Condici�n: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 168 pp. Englisch. N� de ref. del art�culo: 9783642121524

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Banach Spaces and Descriptive Set Theory: Selected Topics (Lecture Notes in Mathematics, 1993)

Dodos, Pandelis

Publicado por Springer, 2010

ISBN 10: 3642121527 ISBN 13: 9783642121524

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Banach Spaces and Descriptive Set Theory: Selected Topics

Pandelis Dodos

Publicado por Springer, Berlin, Springer Berlin Heidelberg, Springer, 2010

ISBN 10: 3642121527 ISBN 13: 9783642121524

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Librería: AHA-BUCH GmbH, Einbeck, Alemania

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Taschenbuch. Condici�n: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. N� de ref. del art�culo: 9783642121524

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Banach Spaces and Descriptive Set Theory: Selected Topics

Pandelis Dodos

Publicado por Springer Berlin Heidelberg, 2010

ISBN 10: 3642121527 ISBN 13: 9783642121524

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Kartoniert / Broschiert. Condici�n: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. - author has been a central player in new developments of this area- This book is a much needed expositionThese 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 . N� de ref. del art�culo: 5049774

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