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Full 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.
Contents
1: Basics and prerequisites
2: Low dimensional spaces
3: Strict and uniform convexity
4: Smoothness and uniform smoothness
5: Uniform smoothness vs uniform convexity
6: Projections on balls and convex sets
7: More moduli and coefficients
8: Radius vs diameter
9: Three special topics
10: Measures of noncompactness and related properties
11: The case of Banach lattices