论文标题
Lipschitz p-summing多线性操作员对应于Lipschitz P-Summing Operator
Lipschitz p-summing multilinear operators correspond to Lipschitz p-summing operators
论文作者
论文摘要
我们提供的条件可以确保在给定设置中满足冰台的统治的操作员在不同的环境中也满足了piestch的统治。由此，我们得出的是，当且仅当映射$ f_t（x_1 \ otimes \ cdots \ otimes x_n）时，有界的mutlirinear operator $ t $ t $是lipschitz $ p $ -smumming。结果基于投影张量规范。提供了Hilbert Tensor Narm的一个例子，以表明当考虑了探测性张量规范以外的合理交叉总体时，该陈述可能无法成立。
We give conditions that ensure that an operator satisfying a Piestch domination in a given setting also satisfies a Piestch domination in a different setting. From this we derive that a bounded mutlilinear operator $T$ is Lipschitz $p$-summing if and only if the mapping $ f_T(x_1\otimes\cdots \otimes x_n):=T(x_1,\ldots, x_n)$ is Lipschitz $p$-summing. The results are based on the projective tensor norm. An example with the Hilbert tensor norm is provided to show that the statement may not hold when a reasonable cross-norm other than the projective tensor norm is considered.
