\(c_{0}\)-singular and \(\ell_{1}\)-singular operators between vector-valued Banach lattices (Q548201)

The author abstracts the results of Kwapien and Pisier concerning the presence of an isomorphic copy of \(c_0\) in vector-valued \(L_p\)-spaces. He uses the pointwise extension of an operator \(T\) between Banach spaces \(X\) and \(Y\) to the operator \(T_E\) between \(E(X)\) and \( E(Y)\), where \(E\) is a vector lattice of measurable functions. If \(E\) does not contain \(c_0\), then \(T\) is an isomorphism of a subspace isomorphic to \(c_0\) if and only if so is \(T_E\). Similar results are possible within Boolean valued analysis.