A refinement of a lemma by Aron, Cascales, and Kozhushkina on Asplund operators

Abstract

We prove a refinement of a lemma by Aron, Cascales, and Kozhushkina on Asplund operators. Refinements of a Bishop–Phelps–Bollobás type theorem for Asplund operators with values in spaces C₀(L) by the same authors, and an extension of this theorem for Asplund operators with values in uniform algebras by Cascales, Guirao, and Kadets, follow.