Non-unique inclusion in a flow and vast centralizer of a generic measure-preserving transformation

A "typical" contraction is unitary

“…This is an operator theoretic analogue of a result of King [9] from ergodic theory. See also Ageev [1] and Stepin, Eremenko [14] for related results.…”

Extensions of generic measure-preserving actions

“…Though it will not be needed in this paper, we mention for completeness a recent result of Solecki [18], who proved that the centralizer of a generic element of Aut(X, µ) is a continuous homomorphic image of a closed subspace of L 0 (R) and contains an increasing sequence of finite dimensional tori whose union is dense (in [18], Solecki explains how to use this result to derive the theorem of Stepin-Eremenko quoted above, which is not explicitly proved in [19] even though it is stated in the abstract of that paper and can also be derived from the authors' arguments).…”

“…[13,14,19,20]); below we quickly discuss this approach, as well as the technique used in [15], and compare the two. Proof.…”

Embedding operators into strongly continuous semigroups

“…This is a difficult problem which has analogues in other areas of mathematics like ergodic theory (see e.g. King [12], de la Rue, de Sam Lazaro [3], Stepin, Eremenko [13]), stochastics and measure theory (see e.g. Heyer [11,Chapter III], Fischer [7]).…”

“…This result is an operator-theoretical counterpart to a recent result of de la Rue and de Sam Lasaro [3] from ergodic theory stating that a "typical" measure preserving transformation can be embedded into a measure preserving flow. We refer to Stepin, Eremenko [13] for further results and references.…”