Absolutely Summing Operators (Cambridge Studies in Advanced Mathematics, Series Number 43) (Volume 0)

We can best understand many fundamental processes in analysis by studying and comparing the summability of series in various modes of convergence. This text provides the reader 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 relevant applications to harmonic analysis, probability and measure theory, and operator theory. This is the first time that the subject and its applications have been presented in such complete detail in book form. Graduate students and researchers in real, complex and functional analysis, and probability theory will benefit from this text.

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 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 to operator theory. This is the first time that the subject and its applications have been presented in such complete detail in book form. Graduate students and researchers from real, complex and functional analysis, and probability theory will benefit from perusing this account.