Power boundedness in Banach algebras associated with locally compact groups
Studia Mathematica, Tome 222 (2014) no. 2, p. 165.

Voir la notice de l'article dans European Digital Mathematics Library

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.
Classification : 43A20, 43A40, 22D15, 46J10
Mots-clés : locally compact group, positive definite function, Fourier-Stieltjes algebra, Fourier algebra, -algebra, power bounded element, coset ring, extension property, IN-group, amenable group 
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     author = {E. Kaniuth and A. T. Lau and A. \"Ulger},
     title = {Power boundedness in {Banach} algebras associated with locally compact groups},
     journal = {Studia Mathematica},
     pages = {165},
     publisher = {mathdoc},
     volume = {222},
     number = {2},
     year = {2014},
     zbl = {1306.43004},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/STUMA_2014__222_2_285688/}
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E. Kaniuth; A. T. Lau; A. Ülger. Power boundedness in Banach algebras associated with locally compact groups. Studia Mathematica, Tome 222 (2014) no. 2, p. 165. https://geodesic-test.mathdoc.fr/item/STUMA_2014__222_2_285688/