On Rosenthal's \(\ell^ 1\)-theorem
Rosenthal's \(\ell^ 1\)-theorem can be restated by saying that a bounded sequence \((x_ n)\) in a Banach space admits a subsequence which is weakly Cauchy provided that there are ``many'' arbitrarily small \(\ell^ 1\)-blocks of the \(x_ n\). Here we show that there is even a norm convergent subsequence if these blocks can be chosen such that their length is bounded.
scientific article; zbMATH DE number 566518