Book

Elements of Geometry of Balls in Banach Spaces

Kazimierz Goebel and Stanislaw Prus

Published in print September 2018 | ISBN: 9780198827351
Published online April 2019 | e-ISBN: 9780191866265 | DOI: https://dx.doi.org/10.1093/oso/9780198827351.001.0001
Elements of Geometry of Balls in Banach Spaces

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One of the subjects of functional analysis is classification of Banach spaces depending on various properties of the unit ball. The need of such considerations comes from a number of applications to problems of mathematical analysis. The list of subjects contains: differential calculus in normed spaces, approximation theory, weak topologies and reflexivity, general theory of convexity and convex functions, metric fixed point theory, and others. The aim of this book is to present basic facts from this field. It is addressed to advanced undergraduate and graduate students interested in the subject. For some it may result in further interest, a continuation and deepening of their study of the subject. It may be also useful for instructors running courses on functional analysis, supervising diploma theses or essays on various levels.

Keywords: Banach spaces; balls; geometry

Book.  176 pages.  Illustrated.

Subjects: Pure Mathematics

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Table of Contents

Basics and prerequisites in Elements of Geometry of Balls in Banach Spaces

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Low dimensional spaces in Elements of Geometry of Balls in Banach Spaces

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Strict and uniform convexity in Elements of Geometry of Balls in Banach Spaces

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Smoothness and uniform smoothness in Elements of Geometry of Balls in Banach Spaces

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Uniform smoothness vs uniform convexity in Elements of Geometry of Balls in Banach Spaces

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Projections on balls and convex sets in Elements of Geometry of Balls in Banach Spaces

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More moduli and coefficients in Elements of Geometry of Balls in Banach Spaces

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Radius vs diameter in Elements of Geometry of Balls in Banach Spaces

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Three special topics in Elements of Geometry of Balls in Banach Spaces

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Measures of noncompactness and related properties in Elements of Geometry of Balls in Banach Spaces

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