论文标题
矢量值Lipschitz函数空间中的Daugavet属性
The Daugavet property in spaces of vector-valued Lipschitz functions
论文作者
论文摘要
我们证明，如果公制空间$ m $具有有限的CEP，则$ \ Mathcal f（m）\ wideHat {\ otimes}_πx$具有每个非零Banach Space $ x $的Daugavet属性。例如，如果$ m $是一个偶尔的二元空间，则适用于$ l_1（μ）$空间。如果$ m $具有CEP，则$ l（\ Mathcal f（m），x）= \ lip（m，x）$具有每一个非零的banach space $ x $的Daugavet属性，这表明$ m $是Injextive Banach Space或Hilbert Space的convex子集时的情况。
We prove that if a metric space $M$ has the finite CEP then $\mathcal F(M)\widehat{\otimes}_π X$ has the Daugavet property for every non-zero Banach space $X$. This applies, for instance, if $M$ is a Banach space whose dual is isometrically an $L_1(μ)$ space. If $M$ has the CEP then $L(\mathcal F(M),X)=\Lip(M,X)$ has the Daugavet property for every non-zero Banach space $X$, showing that this is the case when $M$ is an injective Banach space or a convex subset of a Hilbert space.
