论文标题
统一界原理的滤波器依赖版本
Filter-dependent versions of the Uniform Boundedness Principle
论文作者
论文摘要
对于$ \ mathbb n $上的每个过滤器$ \ Mathcal f $，我们介绍和研究对应的统一$ \ Mathcal F $ bundedness internally incevex topological topological vector Space。这些原则将连续线性图序列的经典统一界限原理推广到与$ \ mathbb n $的cofinite子集的fréchet滤波器相吻合时，通过与这些原理相吻合。我们确定过滤器$ \ MATHCAL F $的组合属性，该属性确保每个Fréchet空间中这些均匀的$ \ Mathcal f $结合原则。此外，对于几种类型的Fréchet空间，我们还隔离了$ \ MATHCAL F $的属性，这些属性对于这些统一$ \ Mathcal F $结合原则的有效性所必需。对于每个无限维班克空间$ x $，我们以这种方式获得这些过滤器的精确组合特征$ \ Mathcal f $，相应的统一$ \ MATHCAL F $结合原理对于$ x $而言是正确的。
For every filter $\mathcal F$ on $\mathbb N$, we introduce and study corresponding uniform $\mathcal F$-boundedness principles for locally convex topological vector spaces. These principles generalise the classical uniform boundedness principles for sequences of continuous linear maps by coinciding with these principles when the filter $\mathcal F$ equals the Fréchet filter of cofinite subsets of $\mathbb N$. We determine combinatorial properties for the filter $\mathcal F$ which ensure that these uniform $\mathcal F$-boundedness principles hold for every Fréchet space. Furthermore, for several types of Fréchet spaces, we also isolate properties of $\mathcal F$ that are necessary for the validity of these uniform $\mathcal F$-boundedness principles. For every infinite-dimensional Banach space $X$, we obtain in this way exact combinatorial characterisations of those filters $\mathcal F$ for which the corresponding uniform $\mathcal F$-boundedness principles hold true for $X$.
