On multiparameter weighted ergodic theorem for noncommutative Lp-spaces

Farrukh Mukhamedov; Maksut Mukhamedov; Seyit Temir

doi:10.1016/j.jmaa.2008.01.054

On multiparameter weighted ergodic theorem for noncommutative L_p-spaces

Farrukh Mukhamedov, Maksut Mukhamedov, Seyit Temir

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In the paper we consider T₁, ..., T_d absolute contractions of von Neumann algebra M with normal, semifinite, faithful trace, and prove that for every bounded Besicovitch weight {a (k)}_{k ∈ Nd} and every x ∈ L_p (M) (p > 1) the averagesA_N (x) = frac(1, | N |) underover(∑, k = 1, N) a (k) T^k (x) converge bilaterally almost uniformly in L_p (M).

Original language	English
Pages (from-to)	226-232
Number of pages	7
Journal	Journal of Mathematical Analysis and Applications
Volume	343
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2008.01.054
Publication status	Published - Jul 1 2008
Externally published	Yes

Keywords

Besicovitch weights
Bilaterally almost uniformly
Ergodic theorem
Noncommutative

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2008.01.054

Cite this

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title = "On multiparameter weighted ergodic theorem for noncommutative Lp-spaces",

abstract = "In the paper we consider T1, ..., Td absolute contractions of von Neumann algebra M with normal, semifinite, faithful trace, and prove that for every bounded Besicovitch weight {a (k)}k ∈ Nd and every x ∈ Lp (M) (p > 1) the averagesAN (x) = frac(1, | N |) underover(∑, k = 1, N) a (k) Tk (x) converge bilaterally almost uniformly in Lp (M).",

keywords = "Besicovitch weights, Bilaterally almost uniformly, Ergodic theorem, Noncommutative",

author = "Farrukh Mukhamedov and Maksut Mukhamedov and Seyit Temir",

note = "Funding Information: The first author is partially supported by FCT grant SFRH/BPD/17419/2004. The authors also would like to thank the referee for his useful suggestions which allowed us to improve the text of the paper.",

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AU - Mukhamedov, Farrukh

AU - Mukhamedov, Maksut

AU - Temir, Seyit

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N2 - In the paper we consider T1, ..., Td absolute contractions of von Neumann algebra M with normal, semifinite, faithful trace, and prove that for every bounded Besicovitch weight {a (k)}k ∈ Nd and every x ∈ Lp (M) (p > 1) the averagesAN (x) = frac(1, | N |) underover(∑, k = 1, N) a (k) Tk (x) converge bilaterally almost uniformly in Lp (M).

AB - In the paper we consider T1, ..., Td absolute contractions of von Neumann algebra M with normal, semifinite, faithful trace, and prove that for every bounded Besicovitch weight {a (k)}k ∈ Nd and every x ∈ Lp (M) (p > 1) the averagesAN (x) = frac(1, | N |) underover(∑, k = 1, N) a (k) Tk (x) converge bilaterally almost uniformly in Lp (M).

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KW - Ergodic theorem

KW - Noncommutative

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