The Metric Theory of Tensor Products (Grothendieck's Résumé Revisited) Part 1: Tensor Norms

Abstract

This paper presents the first of a multi-part series of papers on the metric theory of tensor products according to Grothendieck's "Résumé de la theorie metrique des produits tensoriels topologiques "It contains the basics on tensor norms: a discussion of the special character of the injective and the projective norms, fundamental operations on tensor norms, extension of tensor norms to spaces of infinite dimensions.