Power boundedness in Banach algebras associated with locally compact groups

E. Kaniuth, A. T. Lau, and A. Ülger. "Power boundedness in Banach algebras associated with locally compact groups." Studia Mathematica 222.2 (2014): 165-189. <http://eudml.org/doc/285688>.

@article{E2014,
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 L¹-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.},
author = {E. Kaniuth, A. T. Lau, A. Ülger},
journal = {Studia Mathematica},
keywords = {locally compact group; positive definite function; Fourier-Stieltjes algebra; Fourier algebra; -algebra; power bounded element; coset ring; extension property; IN-group; amenable group},
language = {eng},
number = {2},
pages = {165-189},
title = {Power boundedness in Banach algebras associated with locally compact groups},
url = {http://eudml.org/doc/285688},
volume = {222},
year = {2014},
}

TY - JOUR
AU - E. Kaniuth
AU - A. T. Lau
AU - A. Ülger
TI - Power boundedness in Banach algebras associated with locally compact groups
JO - Studia Mathematica
PY - 2014
VL - 222
IS - 2
SP - 165
EP - 189
AB - 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 L¹-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.
LA - eng
KW - locally compact group; positive definite function; Fourier-Stieltjes algebra; Fourier algebra; -algebra; power bounded element; coset ring; extension property; IN-group; amenable group
UR - http://eudml.org/doc/285688
ER -