Operator ideals and three-space properties of asymptotic ideal seminorms

Autor:	Causey, Ryan M., Draga, Szymon, Kochanek, Tomasz
Rok vydání:	2017
Předmět:	Mathematics - Functional Analysis 46B06 46B20 46B28 (Primary) 46B09 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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 $\max\{p,q\}$. Comment: To appear in Trans. Amer. Math. Soc., 45 pp
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1712.04208 Zobrazit plný text záznamu View this record from Arxiv