Dual functors and the Radon-Nikodym property in the category of Banach spaces
Dual functors and the Radon-Nikodym property in the category of Banach spaces
Abstract The notion of duality of functors is used to study and characterize spaces satisfying the Radon-Nikodym property. A theorem of equivalences concerning the Radon-Nikodym property is proved by categorical means; the classical Dunford-Pettis theorem is then deduced using an adjointness argument. The functorial properties of integral operators, compact operators, …