Rosenthal's l_1-theorem states that any bounded sequence in a Banach space that does not contain a weakly Cauchy subsequence admits a subsequence being equivalent to the unit vector base of l_1. In particular, this means that every Banach space either contains a copy of l_1 or has the property that every bounded sequence admits a weakly Cauchy subsequence. Although the statement of Rosenthal's theorem requires just very little background in functional analysis, its proof relies on infinite Ramsey theory.
The aim of the two talks will be to give a sketch of the proof and (if time permits) to discuss some applications, such as the Josefson-Nissenzweig theorem. |