Operators commuting with mixing sequences (Q1305178)

This paper provides sufficient conditions for a family of linear operators on \(L^2\) to ensure the `Gaussian Distribution Property'. Such a family of operators, that in addition satisfies Bourgain's infinite entropy condition [\textit{J.Bourgain}, Isr. J. Math. 63, No. 1, 79-97 (1988; Zbl 0677.60042)], has a very strong non-convergence property. It is helpful to know that the definition of mixing of all orders for a sequence of transformations used here -- Definition 3.5.1 -- does not coincide with the usual notion for the iterates of a single transformation. The usual notion is here called `mixing of all orders of type II'.