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Averaging sequences and modulated ergodic theorems for weakly almost periodic group representations

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Abstract

LetT be a weakly almost periodic (WAP) representation of a locally compact Σ-compact groupG by linear operators in a Banach spaceX, and letM = M(T) be its ergodic projection onto the space of fixed points (i.e.,Mx is the unique fixed point in the closed convex hull of the orbit ofx). A sequence of probabilities Μn is said toaverage T [weakly] if ∫T(t)x dΜ n converges [weakly] toM(T)x for eachx ∃X. We callΜ n [weakly]unitarily averaging if it averages [weakly] every unitary representation in a Hilbert space, and [weakly]WAPRaveraging if it averages [weakly] every WAP representation. We investigate some of the relationships of these notions, and connect them with properties of the regular representation (by translations) in the spaceWAP(G).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel

    Michael Lin

  2. Department of Mathematics, The Pennsylvania State University, 16802, University Park, PA, USA

    Arkady Tempelman

Authors
  1. Michael Lin
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  2. Arkady Tempelman
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Research partially supported by the Israel Science Foundation.

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Lin, M., Tempelman, A. Averaging sequences and modulated ergodic theorems for weakly almost periodic group representations. J. Anal. Math. 77, 237–268 (1999). https://doi.org/10.1007/BF02791262

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  • DOI: https://doi.org/10.1007/BF02791262

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