Properties of sequence spaces in which \(\ell _ 1\) is weakly compactly embedded (Q1084292)

Using gliding humps techniques and the theory of compact operators, it is established that \(\ell_ 1\subset X\) if X is an FK space containing \(\{\delta^ n\}\) and \(\delta^ n\to 0\) weakly in \(X+\ell_ 1,\) thereby answering a question of Bennett proposed in 1974. It is further shown that the reflexive solid BK spaces containing \(\ell_ 1\) are a universal family for the FK spaces in which \(\delta^ n\to 0\) weakly, using known factorization theory of weakly compact operators.