[PDF] Structures In Banach Spaces eBook

Author : William B. Johnson
Publisher : American Mathematical Soc.
Page : 306 pages
File Size : 25,14 MB
Release : 1979
Category : Mathematics
ISBN : 0821822179

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In this paper detailed investigations of spaces with a symmetric basis of finite length and rearrangement invariant function spaces are presented. The emphasis is on questions arising naturally from the theory of [italic]L[italic subscript]p-spaces.

Author : Nassif Ghoussoub
Publisher : American Mathematical Soc.
Page : 123 pages
File Size : 10,54 MB
Release : 1987
Category : Banach spaces
ISBN : 0821824414

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In this memoir, we study the interrelations between the topological, measure theoretical and geometrical structures in certain classes of Banach spaces. The focus is on those spaces whose bounded subsets have arbitrarily norm-small convex combinations of slices. This class contains spaces with the Radon-Nikodym property as well as B-convex Banach spaces. The topological analysis leads to the concept of "first class functions around sets". This extension of the classical notion of Baire-1 functions is developed in a general non-linear setting.

Author : Nigel John Kalton
Publisher : American Mathematical Soc.
Page : 105 pages
File Size : 47,64 MB
Release : 1993
Category : Mathematics
ISBN : 0821825577

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The general problem addressed in this work is to characterize the possible Banach lattice structures that a separable Banach space may have. The basic questions of uniqueness of lattice structure for function spaces have been studied before, but here the approach uses random measure representations for operators in a new way to obtain more powerful conclusions.

Author : Nigel John Kalton
Publisher : Oxford University Press, USA
Page : 105 pages
File Size : 45,39 MB
Release : 2014-08-31
Category : MATHEMATICS
ISBN : 9781470400705

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The general problem addressed in this work is to characterize the possible Banach lattice structures that a separable Banach space may have. The basic questions of uniqueness of lattice structure for function spaces have been studied before, but here the approach uses random measure representations for operators in a new way to obtain more powerful conclusions.

Author : Petr Hájek
Publisher : Walter de Gruyter GmbH & Co KG
Page : 514 pages
File Size : 24,47 MB
Release : 2014-10-29
Category : Mathematics
ISBN : 3110258994

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This book is about the subject of higher smoothness in separable real Banach spaces. It brings together several angles of view on polynomials, both in finite and infinite setting. Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves around two main broad questions: What is the best smoothness of a given Banach space, and its structural consequences? How large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into infinite dimension where measure and compactness are not available? The subject of infinite dimensional real higher smoothness is treated here for the first time in full detail, therefore this book may also serve as a reference book.