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On matrix summation and the pointwise ergodic theorem

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

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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© 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

  • eBook Packages: Springer Book Archive