Elements of Geometry of Balls in Banach Spaces
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Product details:
- Publisher OUP Oxford
- Date of Publication 20 September 2018
- ISBN 9780198827351
- Binding Hardback
- No. of pages172 pages
- Size 236x163x14 mm
- Weight 432 g
- Language English
- Illustrations 30 0
Categories
Short description:
This book forms the basis of a one-semester course for advanced undergraduate or beginning graduate students studying the geometry of balls in Banach spaces.
MoreLong description:
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.
...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.
Table of Contents:
Basics and prerequisites
Low dimensional spaces
Strict and uniform convexity
Smoothness and uniform smoothness
Uniform smoothness vs uniform convexity
Projections on balls and convex sets
More moduli and coefficients
Radius vs diameter
Three special topics
Measures of noncompactness and related properties
The case of Banach lattices
