Power boundedness in Banach algebras associated with locally compact groups

E. Kaniuth ¹   ; A. T. Lau ²   ; A. Ülger ³

¹ Institute of Mathematics University of Paderborn D-33095 Paderborn, Germany
² Department of Mathematical and Statistical Sciences University of Alberta Edmonton, AB, Canada T6G 2G1
³ Department of Mathematics Koc University 34450 Sariyer, İstanbul, Turkey

Studia Mathematica, Tome 222 (2014) no. 2, pp. 165-189

Résumé

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.

Détail

DOI : 10.4064/sm222-2-4

Keywords: locally compact group fourier stieltjes algebra pursuing investigations power bounded elements study extension property power bounded elements discuss structure closed sets coset ring which appear sets power bounded elements algebras noncompact motion groups noncompact in groups polynomial growth share so called power boundedness property finally characterization power bounded elements reduced fourier stieltjes algebra locally compact group containing subgroup which amenable discrete group