Spaceability of sets of p-compact maps

Abstract

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 ℓs whenever F=ℓs. 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.