This two-volume text provides a complete overview of the theory of
Banach spaces, emphasising its interplay with classical and
harmonic analysis (particularly Sidon sets) and probability. The
authors give a full exposition of all results, as well as numerous
exercises and comments to complement the text and aid graduate
students in functional analysis. The book will also be an
invaluable reference volume for researchers in analysis. Volume 1
covers the basics of Banach space theory, operatory theory in
Banach spaces, harmonic analysis and probability. The authors also
provide an annex devoted to compact Abelian groups. Volume 2
focuses on applications of the tools presented in the first volume,
including Dvoretzky's theorem, spaces without the approximation
property, Gaussian processes, and more. In volume 2, four leading
experts also provide surveys outlining major developments in the
field since the publication of the original French edition.
General
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