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The metric theory of tensor products (grthendieck'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.
Mathematics Subject
Classification (2000): 46B28, 46B07, 46B04.
Key words: Reasonable crossnorms;
projective norm; injective norm; integral bilinear form; tensor norm; (metric)
accessibility.
Quaestiones
Mathematicae 25 (2002), 37-72
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.
Mathematics Subject
Classification (2000): 46B28, 46B07, 46B04.
Key words: Reasonable crossnorms;
projective norm; injective norm; integral bilinear form; tensor norm; (metric)
accessibility.
Quaestiones
Mathematicae 25 (2002), 37-72
