Absolutely Summing Operators

Many fundamental processes in analysis are best understood by studying and comparing the summability of series in various modes of convergence. This text provides the beginning graduate student, one with basic knowledge of real and functional analysis, with an account of p-summing and related operators. The account is panoramic, with detailed expositions of the core results and highly non-trivial applications to, for example, harmonic analysis, probability and measure theory, and operator theory. Graduate students and researchers from real, complex and functional analysis, and probability theory will benefit from this account.

Introduction
Unconditioned and absolute summability in Banach spaces
Fundamentals of p-summing operators
Summing operators on Cp-spaces
Operators on Hilbert spaces and summing operators
p-Integral operators
Trace duality
2-Factorable operators
Ultraproducts and local reflexivity
p-Factorable operators
(q, p)-Summing operators
Type and cotype: the basics
Randomised series and almost summing operators
K-Convexity and B-convexity
Spaces with finite cotype
Weakly compact operators on C(K)-spaces
Type and cotype in Banach lattices
Local unconditionality
Summing algebras
Dvoretzky's theorem and factorization of operators
References
Indexes
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Absolutely Summing Operators

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Table of Contents

Supplemental Materials