The metric theory of tensor products (grthendieck's résumé revisited) part 3: vector sequence spaces

Abstract

In this part of our exposition and expansion of Grothendieck's work on the metric theory of tensor products
we look at the behaviour of the injective and surjective tensor norms in the case where one of the
component spaces is a classical sequence space as exposed in Grothendieck's “Sur
certaines classes de suites dans
les espaces de Banach, et
le theorem de Dvoretzky-Rogers”.


Mathematics Subject
Classification (2000):
46B28, 46B45, 47B07.



Key words: Weakly p-summable
sequences; absolutely p-summable sequences; projective tensor product;
injective
tensor product; compact operators.



Quaestiones
Mathematicae 25 (2002), 95-118