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Power boundedness in Banach algebras associated with locally compact groups

Volume 222 / 2014

E. Kaniuth, A. T. Lau, A. Ülger Studia Mathematica 222 (2014), 165-189 MSC: Primary 43A40, 46J10; Secondary 22D15, 43A20. DOI: 10.4064/sm222-2-4

Abstract

Let $G$ be a locally compact group and $B(G)$ the Fourier–Stieltjes algebra of $G$. Pursuing our investigations of power bounded elements in $B(G)$, we study the extension property for power bounded elements and discuss the structure of closed sets in the coset ring of $G$ which appear as $1$-sets of power bounded elements. We also show that $L^1$-algebras of noncompact motion groups and of noncompact IN-groups with polynomial growth do not share the so-called power boundedness property. Finally, we give a characterization of power bounded elements in the reduced Fourier–Stieltjes algebra of a locally compact group containing an open subgroup which is amenable as a discrete group.

Authors

  • E. KaniuthInstitute of Mathematics
    University of Paderborn
    D-33095 Paderborn, Germany
    e-mail
  • A. T. LauDepartment of Mathematical
    and Statistical Sciences
    University of Alberta
    Edmonton, AB, Canada T6G 2G1
    e-mail
  • A. ÜlgerDepartment of Mathematics
    Koc University
    34450 Sariyer, İstanbul, Turkey
    e-mail

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