论文标题
Banach空间总是产生操作员的八面体空间
Banach spaces which always produce octahedral spaces of operators
论文作者
论文摘要
我们表征了那些满足$ l（y，x）$的Banach Spaces $ x $，对于每个非零Banach Space $ y $。他们是那些满足的人，对于每个有限的尺寸子空间$ z $，$ \ ell_ \ infty $在$ x $ of $ x $ of $ \ ell_1 $ -1 $ -ORTONONAL至$ z $的一部分中都可以有限地说明。我们还证明，$ l（y，x）$在每$ y $的情况下都是八人体，并且只有$ l（\ ell_p^n，x）$是\ in \ mathbb n $和$ 1 <p <\ infty $的$ n \ in contaheDral。最后，我们找到了满足上述条件的Banach空间的示例，例如带有八面体标准的$ \ lip（m）$空间，或带有Daugavet属性的$ L_1 $ - 售价。
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 $\Lip(M)$ spaces with octahedral norms or $L_1$-preduals with the Daugavet property.
