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.
In the present paper we prove the “zero-two” law for positive contractions in the Banach-Kantorovich lattices , constructed by a measure with values in the ring of all measurable functions.
We extend the notion of Dobrushin coefficient of ergodicity to positive contractions defined on the L¹-space associated with a finite von Neumann algebra, and in terms of this coefficient we prove stability results for L¹-contractions.
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