Locally compact groups which are amenable as discrete groups
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- Proc. Amer. Math. Soc. 76 (1979), 46-50 Request permission
Abstract:
In the courses of their independent studies of the existence of invariant means which are not topologically invariant, E. Granirer and W. Rudin have considered several properties of a locally compact group G which are satisfied if G is amenable as a discrete group. By applying a result of J. Rosenblatt (together with ideas of Granirer and Rudin) we show some of these properties on G imply that G is amenable as a discrete group.References
- Edmond Granirer, Criteria for compactness and for discreteness of locally compact amenable groups, Proc. Amer. Math. Soc. 40 (1973), 615–624. MR 340962, DOI 10.1090/S0002-9939-1973-0340962-8
- Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0251549
- Theodore Mitchell, Constant functions and left invariant means on semigroups, Trans. Amer. Math. Soc. 119 (1965), 244–261. MR 193523, DOI 10.1090/S0002-9947-1965-0193523-8
- Derek J. S. Robinson, Finiteness conditions and generalized soluble groups. Part 2, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 63, Springer-Verlag, New York-Berlin, 1972. MR 0332990
- Joseph Max Rosenblatt, Invariant means for the bounded measurable functions on a non-discrete locally compact group, Math. Ann. 220 (1976), no. 3, 219–228. MR 397305, DOI 10.1007/BF01431093
- Joseph Max Rosenblatt, Invariant means and invariant ideals in $L_{\infty }(G)$ for a locally compact group $G$, J. Functional Analysis 21 (1976), no. 1, 31–51. MR 0397304, DOI 10.1016/0022-1236(76)90027-6
- Walter Rudin, Invariant means on $L^{\infty }$, Studia Math. 44 (1972), 219–227. MR 304975, DOI 10.4064/sm-44-3-219-227
- Benjamin B. Wells Jr., Homomorphisms and translates of bounded functions, Duke Math. J. 41 (1974), 35–39. MR 336238
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 76 (1979), 46-50
- MSC: Primary 43A07
- DOI: https://doi.org/10.1090/S0002-9939-1979-0534389-9
- MathSciNet review: 534389