Asymptotic smoothness in Banach spaces, three space properties and applications
R. M. Causey,
A. Fovelle,
G. Lancien
Abstract:We study four asymptotic smoothness properties of Banach spaces, denoted Tp, Ap, Np and Pp. We complete their description by proving the missing renorming theorem for Ap. We prove that asymptotic uniform flattenability (property T∞) and summable Szlenk index (property A∞) are three space properties. Combined with the positive results of the first named author, Draga, and Kochanek, and with the counterexamples we provide, this completely solves the three space problem for this family of properties. We also deri… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.