可扩向量值理想与其极小核的重合
Coincidence of extendible vector-valued ideals with their minimal kernel
摘要：
本文给出了多重线性算子的向量值理想的重合结果。更精确地说，如果$\mathfrak A$是$n$ -线性映射的理想，我们给出了下列等式$\mathfrak A(E_1,\dots,E_n;F) = {\mathfrak A}^{min}(E_1,\dots,E_n;F)$等距成立的条件.作为应用，我们得到了在许多情况下单项式构成空间$\mathfrak A(E_1,\dots,E_n;F)$上的Schauder基.几个结构和几何性质也来自使用这个等式。我们应用我们的结果的特殊情况下，$\mathfrak A$是经典的理想的可扩展或Pietsch积分多重线性算子。对向量值齐次多项式的理想也给出了类似的说明。
英文摘要：
We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if $\mathfrak A$ is an ideal of $n$-linear mappings we give conditions for which the following equality $\mathfrak A(E_1,\dots,E_n;F) = {\mathfrak A}^{min}(E_1,\dots,E_n;F)$ holds isometrically. As an application, we obtain in many cases that the monomials form a Schauder basis on the space $\mathfrak A(E_1,\dots,E_n;F)$. Several structural and geometric properties are also derived using this equality. We apply our results to the particular case where $\mathfrak A$ is the classical ideal of extendible or Pietsch-integral multilinear operators. Similar statements are given for ideals of vector-valued homogeneous polynomials.
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