We use a non-commutative generalization of the Banach Principle to show that the classical individual ergodic theorem for subsequences generated by means of uniform sequences can be extended to the von Neumann algebra setting.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-1-3, author = {Semyon Litvinov and Farrukh Mukhamedov}, title = {On individual subsequential ergodic theorem in von Neumann algebras}, journal = {Studia Mathematica}, volume = {147}, year = {2001}, pages = {55-62}, zbl = {0973.46052}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-1-3} }
Semyon Litvinov; Farrukh Mukhamedov. On individual subsequential ergodic theorem in von Neumann algebras. Studia Mathematica, Tome 147 (2001) pp. 55-62. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-1-3/