The weak limit semigroup of an operator T is the collection of all weak limit points of its powers, and the paper shows that this collection contains large subsets in generic cases for Koopman, contraction, and positive operators.
Ryzhikov,Self-joinings of rank-one actions and applications, École de Théorie Ergodique, 193–206
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Weak limit semigroup in operator theory and ergodic theory
The weak limit semigroup of an operator T is the collection of all weak limit points of its powers, and the paper shows that this collection contains large subsets in generic cases for Koopman, contraction, and positive operators.