稳定半群的范畴定理
Category theorems for stable semigroups
摘要：
受Halmos和Rohlin关于离散保测变换的经典范畴定理的启发，我们在可分希尔伯特空间上证明了酉和等距C_0-半群的抽象集上的类似结果.更重要的是，我们证明了所有弱稳定酉群（等距半群）的集合是第一范畴，而所有几乎弱稳定酉群（等距半群）的集合对于适当的拓扑是剩余的.
英文摘要：
Inspired by the classical category theorems of Halmos and Rohlin for the discrete measure preserving transformations, we prove analogous results in the abstract setting of unitary and isometric C_0-semigroups on a separable Hilbert space. More presicely, we show that the set of all weakly stable unitary groups (isometric semigroups) is of first category, while the set of all almost weakly stable unitary groups (isometric semigroups) is residual for an appropriate topology.
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