2011/02/14 by Mahya Ghandehari, Ghandehari, Mahya
Mathematics · #43A30 #46J10 #46L07 #47B47 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #math.FA #msc:43A30 #msc:46J10 #msc:46L07 #msc:47B47
paper · pdf · doi:10.48550/arxiv.1102.2667
20 pages
arxiv created 2011/02/14 · openalex publication_date 2011/02/14 · arxiv updated 2011/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Rajchman measures of locally compact Abelian groups are studied for almost a century now, and they play an important role in the study of trigonometric series. Eymard's influential work allowed generalizing these measures to the case of non-Abelian locally compact groups G. The Rajchman algebra of G, which we denote by B0(G), is the set of all elements of the Fourier-Stieltjes algebra that vanish at infinity. In the present article, we characterize the locally compact groups that have amenable Rajchman algebras. We show that B0(G) is amenable if and only if G is compact and almost Abelian. On the other extreme, we present many examples of locally compact groups, such as non-compact Abelian groups and infinite solvable groups, for which B0(G) fails to even have an approximate identity.