On the structure of invertible elements in certain Fourier-Stieltjes algebras

2020/01/22 by Aasaimani Thamizhazhagan, Thamizhazhagan, Aasaimani
Mathematics · #43A30 #43A70 #46J40 #46M20 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:43A30 #msc:43A70 #msc:46J40 #msc:46M20

paper · pdf · doi:10.48550/arxiv.2001.08294

15 pages. Accepted in Studia Mathematica

arxiv created 2020/05/11 · arxiv updated 2020/05/13

Abstract

For a locally compact abelian group G, J. L. Taylor (1971) gave a complete characterization of invertible elements in the measure algebra M(G). Using the Fourier-Stieltjes transform, this characterization can be carried out in the context of Fourier-Stieltjes algebras B(G). We obtain this latter characterization for the Fourier-Stieltjes algebra B(G) of certain classes of locally compact groups, in particular, many totally minimal groups and the ax+b-group.

Related

• Restricted algebras on inverse semigroups III, Fourier algebra
• Fundamental Theorems of Fourier-Stieltjes Transform Defined by Induced Representation on Locally Compact Group
• Characterisations of Fourier and Fourier--Stieltjes algebras on locally compact groups
• L^p-Fourier and Fourier-Stieltjes algebras for locally compact groups
• Fourier-Stieltjes transform defined by induced representation on locally compact groups