Ergodic sequences and a subspace of B(G) (Q1119862)

The authors generalize a result of Blum and Eisenberg on the convergence of a sequence of probability measures \(\mu_ n\) to non-abelian groups G. The relationship of \(B_ I(G)\) (the closure of the linear span of the coefficients of the irreducible representations of G) to AP(G) (the space of all almost periodic functions) and also to \(C_ 0(G)\) is investigated and \(B_ I(G)\) is identified for some special groups (e.g., the Heisenberg group). Some results (concerning ``ergodic'' sequences \(\mu_ n)\) already follow from \textit{V. Losert} and the reviewer [Invent. Math. 50, 65-74 (1978; Zbl 0414.22006), Theorem 1 solves the problem posed at the end of the paper, see also Theorem 3] and from \textit{K. Gröchenig}, \textit{V. Losert} and the reviewer [Lect. Notes Math. 1210, 97-107 (1985; Zbl 0607.60008)].