Fourier-Stieltjes algebra of a topological group
Let \(G\) be a topological (not necessarily locally compact) group and let \(B(G)\) denote its Fourier--Stieltjes algebra, i.e. the linear span of the continuous positive definite complex-valued functions on \(G\). The authors describe the basic properties of \(B(G)\) and evaluate its spectrum. In the case, when there is a reasonable notion of the group \(C^*\)-algebra \(A\) for \(G\) (the authors call such \(A\) a host algebra for \(G\); if \(G\) is locally compact then \(A=C^*(G)\)), it is shown that \(B(G)\) is a pre-dual of the universal enveloping von Neumann algebra of \(A\). Finally, \(B(G)\) is calculated when \(G\) is a projective limit of locally compact groups.
scientific article; zbMATH DE number 6011380
scientific article