Elements of Geometry of Balls in Banach Spaces

by Kazimierz Goebel, Stanislaw Prus

Overview

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 includes: 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 book presents basic facts from this field.

Product Details

ISBN-13:	9780198827351
Publisher:	Oxford University Press
Publication date:	11/13/2018
Pages:	172
Product dimensions:	9.30(w) x 6.10(h) x 0.60(d)

About the Author

Kazimierz Goebel, Professor (emeritus), Maria Curie-Skłodowska University, Lublin, Poland,Stanislaw Prus, Professor, Maria Curie-Skłodowska University, Lublin, Poland

Professor emeritus Kazimierz Goebel obtained his PhD in mathematics in 1967 at Maria Curie-Skłodowska University in Poland. Since 1963, he has been employed by UMCS and has served two three-year terms (1993-1999) as Rector of the university. At the same time, he has served as the President of the Polish Mathematical Society. Professor Goebel is the author of five books and over 70 scientific papers. He is a specialist in nonlinear problems of functional analysis, in particular metric fixed point theory. He has supervised and promoted 15 PhD students and is the visiting professor at several universities in the USA, Italy, Japan, Spain, Australia, Thailand. Moreover, he is a frequent short-term visitor, invited speaker and member of committees to a number of conferences and seminars, workshops and schools all over the world.

Professor Stanislaw Prus graduated from Maria Curie-Skłodowska University, Poland, in 1979. He then obtained a PhD in mathematics in 1984 from the Mathematical Institute of Polish Academy of Science, Warsaw. Since 1979, he has been employed at UMCS and is now the author of over 45 scientific papers. Professor Prus is a specialist in the geometry of Banach spaces and nonlinear problems of functional analysis, and in particular of metric fixed point theory. He is also a frequent invited speaker and a member of committees to a number of conferences and seminars world-wide.

Table of Contents

1. Basics and prerequisites2. Low dimensional spaces3. Strict and uniform convexity4. Smoothness and uniform smoothness5. Uniform smoothness vs uniform convexity6. Projections on balls and convex sets7. More moduli and coefficients8. Radius vs diameter9. Three special topics10. Measures of noncompactness and related properties11. The case of Banach lattices

Editorial Reviews

"...this excellent text covers a variety of attractive and important topics which are presented with elegance and concision. It is a welcome addition to the geometry of Banach spaces literature and can be warmly recommended to all students and faculty with an interest in functional analysis and related areas." — Stephen J. Dilworth, Stephen J. Dilworth

"The book...offers a delightful perspective on the geometric aspects, leading the reader to marvel at the shapes and properties of balls in Banach spaces...suitable for self-study either alongside a traditional functional analysis book or as a standalone text." — Ittay Weiss, Senior Lecturer in Mathematics at the University of Portsmouth, UK, Mathematical Association of America

From the Publisher