On uniformly amenable groups

Wysoczański, Janusz

doi:10.1090/S0002-9939-1988-0934870-X

On uniformly amenable groups
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Proc. Amer. Math. Soc. 102 (1988), 933-938 Request permission

Abstract:

We consider the conditions of the uniform amenability of discrete groups. The equivalence of the uniform Følner and Kesten conditions is proved. Also an example of the group which is amenable but not uniformly amenable is given.

References

Marek Bożejko, Uniformly amenable discrete groups, Math. Ann. 251 (1980), no. 1, 1–6. MR 583820, DOI 10.1007/BF01420276
Erling Følner, On groups with full Banach mean value, Math. Scand. 3 (1955), 243–254. MR 79220, DOI 10.7146/math.scand.a-10442
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
Stefan Heinrich, Ultraproducts in Banach space theory, J. Reine Angew. Math. 313 (1980), 72–104. MR 552464, DOI 10.1515/crll.1980.313.72
V. A. Kaĭmanovič, The spectral measure of transition operator and harmonic functions connected with random walks on discrete groups, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 97 (1980), 102–109, 228–229, 236 (Russian, with English summary). Problems of the theory of probability distributions, VI. MR 602365
V. A. Kaĭmanovich and A. M. Vershik, Random walks on discrete groups: boundary and entropy, Ann. Probab. 11 (1983), no. 3, 457–490. MR 704539, DOI 10.1214/aop/1176993497
Gordon Keller, Amenable groups and varieties of groups, Illinois J. Math. 16 (1972), 257–269. MR 296141
Harry Kesten, Symmetric random walks on groups, Trans. Amer. Math. Soc. 92 (1959), 336–354. MR 109367, DOI 10.1090/S0002-9947-1959-0109367-6
Harry Kesten, Full Banach mean values on countable groups, Math. Scand. 7 (1959), 146–156. MR 112053, DOI 10.7146/math.scand.a-10568