An Analysis upon the Asymptotic Structure of Banach Spaces: A Case Study of Envelope Functions

Exploring the Asymptotic Structures of Banach Spaces using Envelope Functions

Abstract

This research studies the asymptotic structures of Banach spaces through the notion of envelope functions. Analogous to the original ones, a new notion of disjoint-envelope functions is introduced and the properties of these functions in connection to the asymptotic structures are studied. The main result gives a new characterization of asymptotic- spaces in terms of the -behavior of disjoint-permissible vectors of constant coefficients.