Ramsey-theoretic analysis of the conditional structure of weakly-null sequences

Abstract

Understanding the possible conditional structure in a given weakly-null sequence $(x_i)$ in some normed space $X$ lies in the heart of several classical problems of this area of mathematics. We will expose the set-theoretic and Ramsey-theoretic methods relevant to both the lack and the existence of this conditional structure. We will concentrate on more recent results and will point out problems for further study.