Operator ideals and three-space properties of asymptotic ideal seminorms

0505054 - MÚ 2020 RIV US eng J - Journal Article
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
R&D Projects: GA ČR GF16-34860L
Institutional support: RVO:67985840
Keywords : Szlenk index * Szlenk power type * three-space property * operator ideals
OECD category: Pure mathematics
Impact factor: 1.363, year: 2019
Method of publishing: Limited access
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 $max {p,q}$.
Permanent Link: http://hdl.handle.net/11104/0296574