Operator ideals and three-space properties of asymptotic ideal seminorms

18 Nov 2018  ·  Causey Ryan M., Draga Szymon, Kochanek Tomasz ·

We introduce asymptotic analogues of the Rademacher and martingale type and cotype of Banach spaces and operators acting on them. Some classical local theory results related, for example, to the `automatic-type' phenomenon, the type-cotype duality, or the Maurey-Pisier theorem, are extended to the asymptotic setting... We also investigate operator ideals corresponding to the asymptotic subtype/subcotype. As an application of this theory, we provide a sharp version of a result of Brooker and Lancien by showing that any twisted sum of Banach spaces with Szlenk power types $p$ and $q$ has Szlenk power type $\max\{p,q\}$. read more

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Functional Analysis