Linear and continuous operators on Köthe–Bochner spaces

Abstract

The Köthe–Bochner spaces Lρ(E) are the vector valued version of the scalar Köthe spaces Lρ, which generalize the Lebesgue spaces L , the Orlicz spaces and many other functional spaces. In the present paper we study the linear and continuous operators U : Lρ(E) → F , giving integral representations for them. These operators generate operators V : Lρ → L(E,F ) which we call “natural operators” and study here.