Let G be a locally compact group, and denote by WAP(M(G)) and AP(M(G)) the spaces of weakly almost periodic, respectively, almost periodic functionals on the measure algebra M(G). Problem 3 in [H.G. Dales, A.T.-M. Lau, D. Strauss, Second duals of measure algebras, Dissertationes Math. (Rozprawy Mat.) 481 (2012), 1–121] asks if WAP(M(G)) and AP(M(G)) admit topological invariant means, and if yes, whether they are unique. The questions regarding existence had already been raised in [M. Daws, Characterising weakly almost periodic functionals on the measure algebra, Studia Math. 204 (2011), no. 3, 213–234]. We answer all these problems in the affirmative.

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Persistent URL dx.doi.org/10.1090/proc/13671
Journal Proceedings of the American Mathematical Society
Citation
Neufang, T. (2017). Topological invariant means on almost periodic functionals: Solution to problems by Dales–Lau–Strauss and daws. Proceedings of the American Mathematical Society, 145(8), 3595–3598. doi:10.1090/proc/13671