Operator ideals and three-space properties of asymptotic ideal seminorms

0505054 - MÚ 2020 RIV US eng J - Článek v odborném periodiku
Causey, R. - Draga, Szymon - Kochanek, T.
Operator ideals and three-space properties of asymptotic ideal seminorms.
American Mathematical Society. Transactions. Roč. 371, č. 11 (2019), s. 8173-8215. ISSN 0002-9947. E-ISSN 1088-6850
Grant CEP: GA ČR GF16-34860L
Institucionální podpora: RVO:67985840
Klíčová slova: Szlenk index * Szlenk power type * three-space property * operator ideals
Obor OECD: Pure mathematics
Impakt faktor: 1.363, rok: 2019
Způsob publikování: Omezený přístup
http://dx.doi.org/10.1090/tran/7759

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 $max {p,q}$.
Trvalý link: http://hdl.handle.net/11104/0296574