Maurey’s Factorization Theory for Operator Spaces

In Banach space theory probabilistic techniques play a central role. For example in the local theory of Banach spaces, geometric properties of finite dimensional subspaces are proved from probabilistic inequalities. The probabilistic approach not only enriched Banach space theory, but also introduced Banach space techniques in other areas such as probability or convex geometry. A famous instance of such interplay is Maurey/Pisier’s theory of type and cotype. Their results are certainly inspired by Rosenthal’s work on subspaces of Lp. On the other hand, the latter is strongly influenced by Grothendieck’s notion of absolutely summing maps, extended by Pietsch to p > 1 and further developed by Lindenstrauss/Pelczynski in their fundamental work on Grothendieck’s inequality.