Amenability properties of Rajchman algebras (Q2841860)

In this interesting paper, the author investigates the Rajchman algebra \(B_0(G)\) of a locally compact group \(G\). \(B_0(G)\) is the set of all elements of the Fourier-Stieltjes algebra that vanish at infinity. The author obtains a characterization of the locally compact groups that have amenable Rajchman algebra. In fact, the author shows that \(B_0(G)\) is amenable iff \(G\) is compact and almost abelian. The author also shows that the Rajchman algebra of a non-discrete locally compact abelian group does not have an approximate identity, which implies that it is not amenable. This way, the author provides large classes of locally compact groups such as non-compact connected SIN groups and infinite solvable groups for which Rajchman algebras are not operator amenable.NEWLINENEWLINEThis paper is quite important as it can throw more light on the problem of operator amenability of Fourier-Stieltjes algebras.