2004/07/28 by Jörg Wenzel, Wenzel, Jörg
Mathematics · #46B04 (Primary) #46B20 #47A63 (Secondary) #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #math.FA #msc:46B04 #msc:46B20 #msc:47A63
paper · pdf · doi:10.48550/arxiv.math/0407482
11 pages
arxiv created 2004/07/28 · openalex publication_date 2004/07/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce stronger versions of the usual notions of martingale type p <= 2 and cotype q >= 2 of a Banach space X and show that these concepts are equivalent to uniform p-smoothness and q-convexity, respectively. All these are metric concepts, so they depend on the particular norm in X. These concepts allow us to get some more insight into the fine line between X being isomorphic to a uniformly p-smooth space or being uniformly p-smooth itself. Instead of looking at Banach spaces, we consider linear operators between Banach spaces right away. The situation of a Banach space X can be rediscovered from this by considering the identity map of X.