On noncommutative weighted local ergodic theorems on Lp-spaces

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 x ∊ Lp(M, τ), that the averages 1/T ∫0Tb(t)αt(x)dt converge bilateral almost uniformly in Lp (M, τ) as T → 0.

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