A note on natural tensor products containing complemented copies of \(c_0\) (Q1356824)

Summary: Let \(H\) be a Fréchet lattice containing a positive sequence equivalent to the unit basis of \(c_0\). We prove that the natural tensor product \(H\underset\mu{\widehat{\otimes}} X\) contains a complemented subspace isomorphic to \(c_0\) for every infinite-dimensional Banach space \(X\), which generalizes a previous result of Cembranos and Freniche.