Injective Dual Banach Spaces and Operator Ideals

Abstract

We give characterizations of Banach spaces with $$\lambda $$ -injective biduals in terms of operators with an integral representation. These results may be thought of as a certain refinement of Lindenstrauss’ extension theorems from his 1964 memoir. We also obtain dual results characterizing Banach spaces with $$\lambda $$ -injective duals in terms of factorization of operators through $$L_1(\mu )$$ or $$\ell _1$$ .