Abstract

We study topological measures on classes of subspaces of an inner product space. The existence of topological measures is discussed, and their relation to measures on orthoprojections from \(\mathcal{B}(H)^{\textrm{pr}}\) is considered, where \(H\) is the completion of the inner product space in question. We also find properties of topological measures defined on classes of splitting and (co)complete subspaces of an inner product space.

中文翻译：

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内积空间子空间类拓扑测度的性质

摘要

我们研究内积空间的子空间类的拓扑测度。讨论了拓扑测度的存在，并考虑了它们与来自\(\mathcal{B}(H)^{\textrm{pr}}\) 的正射投影测度的关系，其中\(H\)是有问题的内积空间。我们还找到了定义在分裂类和内积空间的（共）完备子空间上的拓扑测度的性质。