论文标题
关于多线性操作员高理想的线性函数的表示
On the representation of linear functionals on hyper-ideals of multilinear operators
论文作者
论文摘要
产生多个有用结果的无限尺寸全体形状中的一种标准技术使用Borel变换来代表Banach空间之间的多线性操作员的某些空间中的线性函数，作为多线性操作员。在本文中，我们开发了一种技术来代表线性函数，作为线性操作员，在超出标准技术范围的多线性操作员的空间上。提供了一些精心研究的多线性操作员的混凝土应用，包括紧凑的多线性操作员以及一个新类。我们可以看到，尤其是，有时我们的表示在条件下的限制性少于相关古典的限制。
A standard technique in infinite dimensional holomorphy, which produced several useful results, uses the Borel transform to represent linear functionals on certain spaces of multilinear operators between Banach spaces as multilinear operators. In this paper we develop a technique to represent linear functionals, as linear operators, on spaces of multilinear operators that are beyond the scope of the standard technique. Concrete applications to some well studied classes of multilinear operators, including the class of compact multilinear operators, and to one new class are provided. We can see, in particular, that sometimes our representations hold under conditions less restrictive than those of the related classical ones.
