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On matrix summation and the pointwise ergodic theorem

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Théorie Ergodique

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 532))

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Abstract

For any contraction T in a space L1 there exists a matrix summation method A stronger than the Cesàro method such that for all f∈L1 the A-limit of Tkf exists a.e.. Here we answer the question of existence of a universal A, which works for all T, negatively.

Research supported by the National Science Foundation Grant GP-28683

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References

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Author notes

  1. Chr. Grillenberger & U. Krengel

    Present address: Institut für Mathematische Statistik, Lotzestr. 13, 34 Göttingen, Federal Republic of Germany

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    1. Chr. Grillenberger
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    2. U. Krengel
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    Jean-Pierre Conze Michael S. Keane

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    © 1976 Springer-Verlag

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    Grillenberger, C., Krengel, U. (1976). On matrix summation and the pointwise ergodic theorem. In: Conze, JP., Keane, M.S. (eds) Théorie Ergodique. Lecture Notes in Mathematics, vol 532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080174

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    • DOI: https://doi.org/10.1007/BFb0080174

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    • Publisher Name: Springer, Berlin, Heidelberg

    • Print ISBN: 978-3-540-07803-6

    • Online ISBN: 978-3-540-38217-1

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