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

Michael Lin, Arkady Tempelman

Research output: Contribution to journalArticle

6 Scopus citations

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 {μn} is said to average T [weakly] if ∫ T(t)χ dμn converges [weakly] to M(T)χ for each χ ∈ X. We call {μn} [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 languageEnglish (US)
Pages (from-to)237-268
Number of pages32
JournalJournal d'Analyse Mathematique
Volume77
DOIs
StatePublished - Jan 1 1999

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics(all)

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