Order convergence ergodic theorems in rearrangement invariant spaces

Mustafa Muratov; Julia Pashkova; Ben Zion Rubshtein

doi:10.1007/978-3-0348-0531-5_7

Order convergence ergodic theorems in rearrangement invariant spaces

Mustafa Muratov, Julia Pashkova, Ben Zion Rubshtein

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

We find necessary and sufficient conditions for order convergence of Cesáro averages of positive absolute contractions in rearrangement invariant spaces. We study the case, when the considered measure is infinite. The investigation of order convergence includes both Dominated and Individual Ergodic Theorems.

Original language	English
Title of host publication	Operator Methods in Mathematical Physics - Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2010
Editors	Jan Janas, Pavel Kurasov, Ari Laptev, Sergei Naboko
Publisher	Springer International Publishing
Pages	123-142
Number of pages	20
ISBN (Print)	9783034805308
DOIs	https://doi.org/10.1007/978-3-0348-0531-5_7
State	Published - 1 Jan 2013
Event	5th International Conference: Operator Theory, Analysis and Mathematical Physics, OTAMP 2010 - Bedlewo, Poland Duration: 5 Aug 2010 → 12 Aug 2010

Publication series

Name	Operator Theory: Advances and Applications
Volume	227
ISSN (Print)	0255-0156
ISSN (Electronic)	2296-4878

Conference

Conference	5th International Conference: Operator Theory, Analysis and Mathematical Physics, OTAMP 2010
Country/Territory	Poland
City	Bedlewo
Period	5/08/10 → 12/08/10

Keywords

Ergodic theorems
Order convergence
Positive absolute contraction
Rearrangement invariant spaces

ASJC Scopus subject areas

Analysis

Access to Document

10.1007/978-3-0348-0531-5_7

Cite this

Muratov, M., Pashkova, J., & Rubshtein, B. Z. (2013). Order convergence ergodic theorems in rearrangement invariant spaces. In J. Janas, P. Kurasov, A. Laptev, & S. Naboko (Eds.), Operator Methods in Mathematical Physics - Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2010 (pp. 123-142). (Operator Theory: Advances and Applications; Vol. 227). Springer International Publishing. https://doi.org/10.1007/978-3-0348-0531-5_7

Muratov, Mustafa ; Pashkova, Julia ; Rubshtein, Ben Zion. / Order convergence ergodic theorems in rearrangement invariant spaces. Operator Methods in Mathematical Physics - Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2010. editor / Jan Janas ; Pavel Kurasov ; Ari Laptev ; Sergei Naboko. Springer International Publishing, 2013. pp. 123-142 (Operator Theory: Advances and Applications).

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keywords = "Ergodic theorems, Order convergence, Positive absolute contraction, Rearrangement invariant spaces",

author = "Mustafa Muratov and Julia Pashkova and Rubshtein, {Ben Zion}",

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Muratov, M, Pashkova, J & Rubshtein, BZ 2013, Order convergence ergodic theorems in rearrangement invariant spaces. in J Janas, P Kurasov, A Laptev & S Naboko (eds), Operator Methods in Mathematical Physics - Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2010. Operator Theory: Advances and Applications, vol. 227, Springer International Publishing, pp. 123-142, 5th International Conference: Operator Theory, Analysis and Mathematical Physics, OTAMP 2010, Bedlewo, Poland, 5/08/10. https://doi.org/10.1007/978-3-0348-0531-5_7

Order convergence ergodic theorems in rearrangement invariant spaces. / Muratov, Mustafa; Pashkova, Julia; Rubshtein, Ben Zion.
Operator Methods in Mathematical Physics - Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2010. ed. / Jan Janas; Pavel Kurasov; Ari Laptev; Sergei Naboko. Springer International Publishing, 2013. p. 123-142 (Operator Theory: Advances and Applications; Vol. 227).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Order convergence ergodic theorems in rearrangement invariant spaces

AU - Muratov, Mustafa

AU - Pashkova, Julia

AU - Rubshtein, Ben Zion

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We find necessary and sufficient conditions for order convergence of Cesáro averages of positive absolute contractions in rearrangement invariant spaces. We study the case, when the considered measure is infinite. The investigation of order convergence includes both Dominated and Individual Ergodic Theorems.

AB - We find necessary and sufficient conditions for order convergence of Cesáro averages of positive absolute contractions in rearrangement invariant spaces. We study the case, when the considered measure is infinite. The investigation of order convergence includes both Dominated and Individual Ergodic Theorems.

KW - Ergodic theorems

KW - Order convergence

KW - Positive absolute contraction

KW - Rearrangement invariant spaces

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SN - 9783034805308

T3 - Operator Theory: Advances and Applications

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BT - Operator Methods in Mathematical Physics - Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2010

A2 - Janas, Jan

A2 - Kurasov, Pavel

A2 - Laptev, Ari

A2 - Naboko, Sergei

PB - Springer International Publishing

T2 - 5th International Conference: Operator Theory, Analysis and Mathematical Physics, OTAMP 2010

Y2 - 5 August 2010 through 12 August 2010

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Muratov M, Pashkova J, Rubshtein BZ. Order convergence ergodic theorems in rearrangement invariant spaces. In Janas J, Kurasov P, Laptev A, Naboko S, editors, Operator Methods in Mathematical Physics - Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2010. Springer International Publishing. 2013. p. 123-142. (Operator Theory: Advances and Applications). doi: 10.1007/978-3-0348-0531-5_7

Order convergence ergodic theorems in rearrangement invariant spaces

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