Approximation numbers of nuclear operators and geometry of Banach spaces (Q1193252)

We give conditions on Banach spaces \(E\) and \(F\) which guarantee that, for every nuclear operator from \(E\) into \(F\), the sequence of approximation numbers belongs to the Marcinkiewicz space \(\ell_{s,\infty}\) with \(1\leq s<\infty\).