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  • Author or Editor: Farrukh Mukhamedov x
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We prove that unique ergodicity of tensor product of a C *-dynamical system implies its strictly weak mixing. By means of this result a uniform weighted ergodic theorem with respect to S -Besicovitch sequences for strictly weak mixing dynamical systems is proved. Moreover, we provide certain examples of strictly weak mixing dynamical systems.

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In the present paper we consider a von Neumann algebra M with a faithful normal semi-finite trace τ, and {α t}, a strongly continuous extension to L p(M, τ) of a semigroup of absolute contractions on L 1(M, τ). By means of a non-commutative Banach Principle we prove for a Besicovitch function b and xL p(M, τ), that the averages 1/T0 T b(t)α t(x)dt converge bilateral almost uniformly in L p (M, τ) as T → 0.

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