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Criteria for compactness and for discreteness of locally compact amenable groups. (English) Zbl 0274.22009

MSC:
22D15 Group algebras of locally compact groups
22D35 Duality theorems for locally compact groups
43A07 Means on groups, semigroups, etc.; amenable groups
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[1] Mahlon M. Day, Amenable semigroups, Illinois J. Math. 1 (1957), 509 – 544. · Zbl 0078.29402
[2] Erling Følner, On groups with full Banach mean value, Math. Scand. 3 (1955), 243 – 254. · Zbl 0067.01203 · doi:10.7146/math.scand.a-10442 · doi.org
[3] Erling Følner, Note on groups with and without full Banach mean value, Math. Scand. 5 (1957), 5 – 11. · Zbl 0080.31903 · doi:10.7146/math.scand.a-10482 · doi.org
[4] Edmond E. Granirer, Exposed points of convex sets and weak sequential convergence, American Mathematical Society, Providence, R.I., 1972. Applications to invariant means, to existence of invariant measures for a semigroup of Markov operators etc. . ; Memoirs of the American Mathematical Society, No. 123. · Zbl 0258.46001
[5] E. Granirer, On finite equivalent invariant measures for semigroups of transformations, Duke Math. J. 38 (1971), 395 – 408. · Zbl 0218.43002
[6] 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. · Zbl 0174.19001
[7] Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. · Zbl 0416.43001
[8] I. Namioka, Følner’s conditions for amenable semi-groups, Math. Scand. 15 (1964), 18 – 28. · Zbl 0138.38001 · doi:10.7146/math.scand.a-10723 · doi.org
[9] I. Namioka, On certain actions of semi-groups on \?-spaces, Studia Math. 29 (1967), 63 – 77. · Zbl 0232.22009
[10] James C. S. Wong, Topologically stationary locally compact groups and amenability, Trans. Amer. Math. Soc. 144 (1969), 351 – 363. · Zbl 0202.02802
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