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  • 1 International Islamic University Malaysia Department of Computational & Theoretical Sciences Faculty of Sciences P.O. Box, 141 25710 Kuantan, Pahang Malaysia
  • 2 Tashkent Institute of Textile and Light Industry Department of Mathematics Tashkent 700100 Uzbekistan
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In the present paper we consider a von Neumann algebra M with a faithful normal semi-finite trace τ, and {αt}, a strongly continuous extension to Lp(M, τ) of a semigroup of absolute contractions on L1(M, τ). By means of a non-commutative Banach Principle we prove for a Besicovitch function b and xLp(M, τ), that the averages 1/T0Tb(t)αt(x)dt converge bilateral almost uniformly in Lp (M, τ) as T → 0.