The isometric theory of classical Banach spaces
Author: H. Elton Lacey
Publisher:
Published: 1972
Total Pages: 880
ISBN-13:
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Author: H. Elton Lacey
Publisher:
Published: 1972
Total Pages: 880
ISBN-13:
DOWNLOAD EBOOKAuthor: H.E. Lacey
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 281
ISBN-13: 3642657621
DOWNLOAD EBOOKThe purpose of this book is to present the main structure theorems in the isometric theory of classical Banach spaces. Elements of general topology, measure theory, and Banach spaces are assumed to be familiar to the reader. A classical Banach space is a Banach space X whose dual space is linearly isometric to Lp(j1, IR) (or Lp(j1, CC) in the complex case) for some measure j1 and some 1 ~ p ~ 00. If 1
Author: J. Lindenstrauss
Publisher: Springer Science & Business Media
Published: 2013-12-11
Total Pages: 253
ISBN-13: 3662353474
DOWNLOAD EBOOKAuthor: J. Lindenstrauss
Publisher: Springer Science & Business Media
Published: 2013-11-11
Total Pages: 202
ISBN-13: 3642665578
DOWNLOAD EBOOKThe appearance of Banach's book [8] in 1932 signified the beginning of a syste matic study of normed linear spaces, which have been the subject of continuous research ever since. In the sixties, and especially in the last decade, the research activity in this area grew considerably. As a result, Ban:ach space theory gained very much in depth as well as in scope: Most of its well known classical problems were solved, many interesting new directions were developed, and deep connections between Banach space theory and other areas of mathematics were established. The purpose of this book is to present the main results and current research directions in the geometry of Banach spaces, with an emphasis on the study of the structure of the classical Banach spaces, that is C(K) and Lip.) and related spaces. We did not attempt to write a comprehensive survey of Banach space theory, or even only of the theory of classical Banach spaces, since the amount of interesting results on the subject makes such a survey practically impossible.
Author: Joram Lindenstrauss
Publisher: Springer
Published: 2006-11-15
Total Pages: 254
ISBN-13: 3540377328
DOWNLOAD EBOOKSpringer-Verlag began publishing books in higher mathematics in 1920, when the series Grundlehren der mathematischen Wissenschaften, initially conceived as a series of advanced textbooks, was founded by Richard Courant. A few years later a new series Ergebnisse der Mathematik und ihrer Grenzgebiete, survey reports of recent mathematical research, was added. Of over 400 books published in these series, many have become recognized classics and remain standard references for their subject. Springer is reissuing a selected few of these highly successful books in a new, inexpensive sofcover edition to make them easily accessible to younger generations of students and researchers.
Author: Joram Lindenstrauss
Publisher: Springer
Published: 1977
Total Pages: 264
ISBN-13: 9783540088882
DOWNLOAD EBOOKAuthor:
Publisher: Elsevier
Published: 2003-05-06
Total Pages: 873
ISBN-13: 0080533507
DOWNLOAD EBOOKHandbook of the Geometry of Banach Spaces
Author: Pandelis Dodos
Publisher: Springer
Published: 2010-04-15
Total Pages: 180
ISBN-13: 3642121535
DOWNLOAD EBOOKThese 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.
Author: Sylvia Guerre-Delabriere
Publisher: CRC Press
Published: 1992-07-21
Total Pages: 234
ISBN-13: 9780824787233
DOWNLOAD EBOOKAuthor: H. Elton Lacey
Publisher:
Published: 1974
Total Pages: 270
ISBN-13:
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