The closed ideal of \((c_0, p, q)\)-summing operators
The authors study the closed operator ideal formed by the \((c_0,p,q)\)-summing operators, provided that \(1/p+ 1/q\leq 1\). The identity map \(Id: \ell_{p^*}\to \ell_q\) factors through \(T: X\to Y\) if and only if \(T\) does not belong to this ideal. The associated superideal consists of those maps \(T\) for which all ultrapowers belong to the class of \((c_0,p,q)\)-summing operators. Operators in the complement of this superideal factor the identity maps \(Id: \ell^n_{p^*}\to \ell^n_q\) uniformly.
scientific article; zbMATH DE number 1556616
scientific article