New Classes of Operators Admitting a Perturbative Characterization

Abstract

We study the semigroups $$({\\mathcal {C}}_p)_+$$(Cp)+, $$({\\mathcal {C}}_p^{\\text {dual}})_-$$(Cpdual)-, $${\\mathcal {G}}_-$$G- and $${\\mathcal {H}}_-$$H- associated with the operator ideals $${\\mathcal {C}}_p$$Cp of p-converging operators ($$1<p<\\infty $$1<p<∞), $${\\mathcal {G}}$$G of Grothendieck operators, and $${\\mathcal {H}}$$H of $$c_0$$c0-cosingular operators. We show that these semigroups admit a perturbative characterization and satisfy the 3-operator property.