Banach spaces which always produce octahedral spaces of operators

Abstract

We characterise those Banach spaces X which satisfy that L(Y, X) is octahedral for every non-zero Banach space Y. They are those satisfying that, for every finite dimensional subspace Z, l(infinity) can be finitely-representable in a part of X kind of l(1)-orthogonal to Z. We also prove that L(Y, X) is octahedral for every Y if, and only if, L(l(n)(p), X) is octahedral for every n is an element of N and 1 < p < infinity. Finally, we find examples of Banach spaces satisfying the above conditions like Lip(0)(M) spaces with octahedral norms or L-1-preduals with the Daugavet property.