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On noncommutative weighted local ergodic theorems on |
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| Authors: | Farrukh Mukhamedov Abdusalom Karimov |
| Affiliation: | (1) Department of Computational & Theoretical Sciences Faculty of Sciences, International Islamic University Malaysia, P.O. Box, 141, 25710 Kuantan, Pahang, Malaysia;(2) Department of Mathematics, Tashkent Institute of Textile and Light Industry, Tashkent, 700100, Uzbekistan |
| Abstract: | 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 x ∊ L p (M, τ), that the averages 1/T ∫0 T b(t)α t (x)dt converge bilateral almost uniformly in L p (M, τ) as T → 0. Communicated by Dénes Petz |
| Keywords: | local ergodic theorem the Banach Principle Besicovitch function |
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