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Weighted Ergodic Theorem for Contractions of Orlicz–Kantorovich lattice \(L_{M}(\widehat{\nabla },\widehat{\mu }\))

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Abstract

In the present paper, we prove a Besicovich weighted ergodic theorem for positive contractions acting on Orlich–Kantorovich space. Our main tool is the use of methods of measurable bundles of Banach–Kantorovich lattices.

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Acknowledgments

The first named author (I.G.) acknowledges the IIUM-RMC grant EDW B 11-185-0663. The second named author (F.M.) acknowledges the MOHE Grant ERGS13-024-0057. He also thanks the Junior Associate scheme of the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy.

Finally, the author also would like to thank to anonymous referees whose useful suggestions and comments improve the content of the paper.

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Authors and Affiliations

  1. Department of Science in Engineering, Faculty of Engineering, International Islamic University Malaysia, P.O. Box 10, 50728, Kuala-Lumpur, Malaysia

    Inomjon Ganiev

  2. Department of Computational & Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P.O. Box 141, 25710, Kuantan, Pahang, Malaysia

    Farrukh Mukhamedov

Authors
  1. Inomjon Ganiev
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  2. Farrukh Mukhamedov
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Correspondence to Farrukh Mukhamedov.

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Communicated by Mohammad Sal Moslehian.

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Ganiev, I., Mukhamedov, F. Weighted Ergodic Theorem for Contractions of Orlicz–Kantorovich lattice \(L_{M}(\widehat{\nabla },\widehat{\mu }\)). Bull. Malays. Math. Sci. Soc. 38, 387–397 (2015). https://doi.org/10.1007/s40840-014-0025-9

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  • DOI: https://doi.org/10.1007/s40840-014-0025-9

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