On left thickness of subsets in semigroups
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- by James C. S. Wong PDF
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Abstract:
We reformulate the concept of left thickness in a semigroup introduced by H. Junghenn in Amenability of function spaces on thick subsemigroups, Proc. Amer. Math. Soc. 75 (1979), 37-41, and obtain a number of interesting new characterisations of left thickness without assuming left amenability. Moreover, these characterisations are similar in nature to familiar characterisations of left amenability on semigroups. We also sharpen some of Junghenn’s results, paving the way for extension to locally compact semigroups.References
- Mahlon M. Day, Amenable semigroups, Illinois J. Math. 1 (1957), 509–544. MR 92128
- Mahlon M. Day, Semigroups and amenability, Semigroups (Proc. Sympos., Wayne State Univ., Detroit, Mich., 1968) Academic Press, New York, 1969, pp. 5–53. MR 0265502
- Mahlon M. Day, Lumpy subsets in left-amenable locally compact semigroups, Pacific J. Math. 62 (1976), no. 1, 87–92. MR 410258 —, Left lumpy to left thick, A guided tour (to appear).
- Jacques Dixmier, Les moyennes invariantes dans les semi-groupes et leurs applications, Acta Sci. Math. (Szeged) 12 (1950), 213–227 (French). MR 37470
- E. Granirer, Extremely amenable semigroups. II, Math. Scand. 20 (1967), 93–113. MR 212551, DOI 10.7146/math.scand.a-10825
- E. Granirer and Anthony T. Lau, Invariant means on locally compact groups, Illinois J. Math. 15 (1971), 249–257. MR 277667 E. Hewitt and K. A. Ross, Abstract harmonic analysis. I, Springer-Verlag, Berlin and New York, 1963.
- H. D. Junghenn, Amenability of function spaces on thick subsemigroups, Proc. Amer. Math. Soc. 75 (1979), no. 1, 37–41. MR 529208, DOI 10.1090/S0002-9939-1979-0529208-0
- H. Kharaghani, Left thick subsets of a topological semigroup, Illinois J. Math. 22 (1978), no. 1, 41–48. MR 463347
- 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
- Theodore Mitchell, Function algebras, means, and fixed points, Trans. Amer. Math. Soc. 130 (1968), 117–126. MR 217577, DOI 10.1090/S0002-9947-1968-0217577-8
- Carroll Wilde and Klaus Witz, Invariant means and the Stone-Čech compactification, Pacific J. Math. 21 (1967), 577–586. MR 212552
- James C. S. Wong, Topologically stationary locally compact groups and amenability, Trans. Amer. Math. Soc. 144 (1969), 351–363. MR 249536, DOI 10.1090/S0002-9947-1969-0249536-4
- James C. S. Wong, Amenability and substantial semigroups, Canad. Math. Bull. 19 (1976), no. 2, 231–234. MR 427948, DOI 10.4153/CMB-1976-036-7
- James C. S. Wong, A characterization of topological left thick subsets in locally compact left amenable semigroups, Pacific J. Math. 62 (1976), no. 1, 295–303. MR 410259
- James C. S. Wong, On topological analogues of left thick subsets in semigroups, Pacific J. Math. 83 (1979), no. 2, 571–585. MR 557955
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 403-407
- MSC: Primary 43A07; Secondary 22A20
- DOI: https://doi.org/10.1090/S0002-9939-1982-0640241-0
- MathSciNet review: 640241