Talk:Characterization of Ergodicity in terms of Koopman Operator

There is a wealth of useful stuff here, but it needs to be unpacked and separated out into sections.

The usual way to do this would be to set up a page for each equivalent statement and transclude appropriately.


 * Do you mean to move all of them into Definition:Ergodic_Measure-Preserving_Transformation? Let me kindly warn that more equivalent statements are going to appear. --Usagiop (talk) 16:31, 7 February 2023 (UTC)

We also really need a page defining the Koopman operator. It's suboptimal to have the basic definition missing for a proof which relies upon its existence. --prime mover (talk) 06:29, 7 February 2023 (UTC)


 * Yes, I will try it.
 * Is is not easy to formulate such a parent page.
 * In my sources, everything defined as $f \mapsto f \circ T$ is roughly called Koopman operator but we need to be careful about:
 * In Definition:Koopman Operator on Complex L-2 Space, the Koopman operator is defined for equivalent classes, because $L^2$ space is a set of equivalent classes.
 * But on this page, the Koopman operator is defined pointwise.
 * Anyway it should be possible and must be done. --Usagiop (talk) 16:31, 7 February 2023 (UTC)