Superreflexivity and J-convexity of Banach spaces
Abstract
A Banach space X is superreflexive if each Banach space Y that is finitely representable in X is reflexive. Superreflexivity is known to be equivalent to J-convexity and to the non-existence of uniformly bounded factorizations of the summation operators Sn through X. We give a quantitative formulation of this equivalence. This can in particular be used to find a factorization of Sn through X, given a factorization of SN through [L2,X], where N is `large' compared to n.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.