  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.
