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Ergodic theorems in fully symmetric spaces of τ-measurable operators

Vladimir Chilin, Semyon Litvinov (2015)

Studia Mathematica

Junge and Xu (2007), employing the technique of noncommutative interpolation, established a maximal ergodic theorem in noncommutative L p -spaces, 1 < p < ∞, and derived corresponding maximal ergodic inequalities and individual ergodic theorems. In this article, we derive maximal ergodic inequalities in noncommutative L p -spaces directly from the results of Yeadon (1977) and apply them to prove corresponding individual and Besicovitch weighted ergodic theorems. Then we extend these results to noncommutative...

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