Abstract

We construct an example of a Hilbert \(C^*\)-module which shows that Troitsky’s theorem on the geometric essence of \( {\mathcal A} \)-compact operators between Hilbert \(C^*\)-modules cannot be extended to modules which are not countably generated case (even in the case of a stronger uniform structure, which is also introduced). In addition, the constructed module admits no frames.

中文翻译：

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具有极值特性的 Hilbert $$C^*$$ -Module

摘要

我们构造了一个 Hilbert \(C^*\) - 模的例子，它表明 Troitsky 的关于\( {\mathcal A} \) - Hilbert \(C^*\) - 模之间的紧算子的几何本质的定理不能扩展到不可数生成的模块的情况下（即使在更强的统一结构的情况下，这也是引入的）。此外，构造的模块不允许任何框架。