Introduction à l'étude des espaces de Banach
The monograph is devoted to the study of Banach spaces with the focus on the interplay of functional analysis and probability theory. It starts with a brief overview of basic facts from Banach space theory and from probability theory. Thirteen chapters are then devoted to more special subjects - Schauder bases, unconditional convergence, Banach space valued random variables, type and cotype of Banach spaces and factorization of operators through a Hilbert space, p-summing operators, properties of spaces Lp, properties of the space ℓ1, euclidean sections and the Dvoretzky theorem, separable spaces without approximation property, gaussian processes, reflexive subspaces of L1, applications of the method of selectors and Pisier's space of almost surely continuous functions. In the appendix basic facts on Banach algebras and compact abelian groups are given.