Abstract
AbstractInspired by the classical category theorems of Halmos and Rohlin for discrete measure-preserving transformations, we prove analogous results in the abstract setting of unitary and isometric C0-semigroups on a separable Hilbert space. More precisely, we show that, for an appropriate topology, 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.
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