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Methods in Banach space theory proceedings of the V Conference on Banach Spaces, Cáceres, Spain, 13-18 September, 2004 by Conference on Banach Spaces (5th 2004 CГЎceres, Spain)

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Published by Cambridge University Press in Cambridge, New York .
Written in English


  • Banach spaces -- Congresses

Book details:

Edition Notes

Includes bibliographical references

Statementedited by Jesús M.F. Castillo, William B. Johnson
SeriesLondon Mathematical Soceity lecture note series -- 337
ContributionsCastillo, Jesús M. F, Johnson, W. B. 1944-
The Physical Object
Paginationx, 357 p. :
Number of Pages357
ID Numbers
Open LibraryOL17206199M
ISBN 100521685680
ISBN 109780521685689

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This book introduces graduate students and resarchers to the study of the geometry of Banach spaces using combinatorial methods. The combinatorial, and in particular the Ramsey-theoretic, approach to Banach space theory is not new, it can be traced back as early as the s.   "This textbook for a two-semester course in functional analysis presents the basic ideas, techniques, and methods that form the underpinnings of the discipline." (SciTech Book News, Vol. 25, No. 3, September ) " a useful book which helps the student to understand Banach space theory.". Many important reference works in Banach space theory have appeared since Banach's "Théorie des Opérations Linéaires", the impetus for the development of much of the modern theory in this field. While these works are classical starting points for the graduate student wishing to do research in. An Introduction to Metric Spaces and Fixed Point Theory includes an extensive bibliography and an appendix which provides a complete summary of the concepts of set theory, including Zorn's Lemma, Tychonoff's Theorem, Zermelo's Theorem, and transfinite induction.

Picture: closing at the main lecture room xi Geometrical Methods --Saturated extensions, the attractors method and Hereditarily James Tree Spaces / Spiros A. Argyros, Alexander D. Arvanitakis, Andreas G. Tolias 1 --The Daugavet property for Lindenstrauss spaces / J. Becerra, M. Martin 91 --Weakly null sequences in the Banach space C(K) / I. A Schauder basis in a Banach space X is a sequence {e n} n ≥ 0 of vectors in X with the property that for every vector x in X, there exist uniquely defined scalars {x n} n ≥ 0 depending on x, such that = ∑ = ∞, = (), ():= ∑. Banach spaces with a Schauder basis are necessarily separable, because the countable set of finite linear combinations with rational coefficients (say) is dense. Hahn–Banach separation theorems are the geometrical versions of the Hahn–Banach Theorem. It has numerous uses in convex geometry, optimization theory, and separation theorem is derived from the original form of the theorem. Let X be a real vector space, A and B subsets of X, ≠ a linear functional on X, α a scalar, and let = − ().If ⁡ ≤ ≤ ⁡ then we say that H (or. This is a short course on Banach space theory with special emphasis on certain aspects of the classical theory. In particular, the course focuses on three major topics: the elementary theory of Schauder bases, an introduction to Lp spaces, and an introduction to C(K) by: