Some Results on Infinite Dimensional Asymptotic Structure of Banach Spaces

Abstract

This thesis presents some results in the newly developed field of infinite dimensional asymptotic structure of Banach spaces. The concept of infinite dimensional asymptotic structure lies between local structure (finite dimensional subspaces) and global structure (infinite dimensional subspaces). The thesis studies finite vector sequences of increasing complexity in an attempt to gradually conduct local information into stronger contexts, sometime even an infinite dimensional context.