Resumen de Banach spaces which always produce octahedral spaces of operators

Abraham Rueda Zoca

• 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, \ell _\infty can be finitely-representable in a part of X kind of \ell _1 -orthogonal to Z. We also prove that L(Y, X) is octahedral for every Y if, and only if, L(\ell _p^n,X) is octahedral for every n\in {\mathbb {N}} and 1 p \infty . Finally, we find examples of Banach spaces satisfying the above conditions like {\textrm{Lip}}_0(M) spaces with octahedral norms or L_1 -preduals with the Daugavet property.