Ergodic theorems in fully symmetric spaces of τ-measurable operators

• Autorzy: Vladimir Chilin , Semyon Litvinov
• Języki publikacji: EN

Abstrakty

EN

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 fully symmetric Banach spaces with the Fatou property and nontrivial Boyd indices, in particular, to noncommutative Lorentz spaces $L_{p,q}$. Norm convergence of ergodic averages in noncommutative fully symmetric Banach spaces is also studied.

Kategorie tematyczne

• 46L52: Noncommutative function spaces
• 47A35: Ergodic theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 228
• Numer: 2
• Strony: 177-195

Daty

wydano

2015

Twórcy

autor

Vladimir Chilin

• National University of Uzbekistan, Tashkent, 700174, Uzbekistan

autor

Semyon Litvinov

• Pennsylvania State University, Hazleton, PA 18202, U.S.A.

Identyfikatory

DOI

10.4064/sm228-2-5