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.

我们刻画那些满足L ( Y ,  X ) 对于每个非零 Banach 空间Y都是八面体的Banach 空间X。它们满足于，对于每个有限维子空间Z，\(\ell _\infty \)可以在X的一部分中有限表示为\(\ell _1\) -正交于Z。我们还证明L ( Y ,  X ) 对于每个Y都是八面体当且仅当\(L(\ell _p^n,X)\)对于每个\(n\in {\mathbb {N} }\)和\(1<p<\infty \)。最后，我们找到满足上述条件的 Banach 空间示例，例如具有八面体范数的\({\textrm{Lip}}_0(M)\)空间或具有 Daugavet 属性的\(L_1\) -preduals。