Geodesic
Uniform convergence on subspaces in von Neumann's ergodic theorem with continuous time
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 183-206

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Power-law uniform (in the operator norm) convergence on vector subspaces with their own norms in von Neumann's ergodic theorem with continuous time is considered. All possible exponents of the considered power-law convergence are found; for each of these exponents, spectral criteria for such convergence are given and a complete description of all such subspaces is obtained. Uniform convergence over the entire space takes place only in trivial cases, which explains the interest in the uniform convergence just on subspaces. In addition, along the way, the old convergence rate estimates in the von Neumann ergodic theorem for (semi)flows are generalized and refined.
Keywords: von Neumann's ergodic theorem, rates of convergence in ergodic theorems, power-law uniform convergence. 
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     title = {Uniform convergence on subspaces in von {Neumann's} ergodic theorem with continuous time},
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A. G. Kachurovskii; I. V. Podvigin; V. E. Todikov. Uniform convergence on subspaces in von Neumann's ergodic theorem with continuous time. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 183-206. http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a29/