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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Power boundedness in Banach algebras associated with locally compact groups

### Tom 222 / 2014

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

#### Streszczenie

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.

#### Autorzy

• E. KaniuthInstitute of Mathematics
e-mail
• A. T. LauDepartment of Mathematical
and Statistical Sciences
University of Alberta