As a follow-up to previous talks on Ramsey-type principles, we will show how Ramsey theory is useful in Banach space theory. We will cover the paradigmatic example of Rosenthal's $\ell_1$ theorem. This celebrated theorem states that every bounded sequence in a Banach space has a weakly Cauchy subsequence if and only if the space does not contain a copy of $\ell_1$.
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