On the subalgebra of a Fourier-Stieltjes algebra generated by pure positive definite functions (Q368534)

For a locally compact group \(G\), Yen-Hei Cheng considered the closed subspace \(a_0 (G)\) which is generated by the pure positive definite functions. In many cases \(a_0 (G)\) is an algebra. Using Heisenberg groups and the \(2\times 2\) real special linear group, the authors illustrate that this is not the case in general. The structures of the algebras thereby created and the properties related to amenability are examined.