Spaceability of sets of p-compact maps

We provide quite sufficient conditions on the Banach spaces \(E\) and \(F\) in order to obtain the spaceability of the set of all linear operators from \(E\) into \(F\) which are \(q\)-compact but not \(p\)-compact. Also, under similar conditions over \(E\), we prove that this set contains (up to the null operator) a copy of \(\ell_s\) whenever \(F = \ell_s\). Finally, we give some applications of our previous results to show the spaceability of some sets formed by non-linear mappings (polynomial and Lipschitz) which are \(q\)-compact but not \(p\)-compact. The spaceability in the space of holomorphic mappings determined by \(p\)-compact sets is also considered.