### Abstract

Let T be a weakly almost periodic (WAP) representation of a locally compact σ-compact group G by linear operators in a Banach space X, and let M = M(T) be its ergodic projection onto the space of fixed points (i.e., Mχ is the unique fixed point in the closed convex hull of the orbit of χ). A sequence of probabilities {μ_{n}} is said to average T [weakly] if ∫ T(t)χ dμ_{n} converges [weakly] to M(T)χ for each χ ∈ X. We call {μ_{n}} [weakly] unitarily averaging if it averages [weakly] every unitary representation in a Hilbert space, and [weakly] WAPR-averaging 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 space WAP(G).

Original language | English (US) |
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Pages (from-to) | 237-268 |

Number of pages | 32 |

Journal | Journal d'Analyse Mathematique |

Volume | 77 |

DOIs | |

State | Published - Jan 1 1999 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematics(all)

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## Cite this

*Journal d'Analyse Mathematique*,

*77*, 237-268. https://doi.org/10.1007/BF02791262