Asymptotic-lp Banach Spaces and the Property of Lebesgue

Abstract

The primary contribution of this work is to nearly characterize the Property of Lebesgue for Banach spaces that behave in a global asymptotic sense like lp. This generalizes a number of individual results that are collected by Russell Gordon in his 1991 survey article among other notable consequences and also raises the possibility of characterizing the Property of Lebesgue for more general Banach spaces in terms of their local asymptotic structurCes.