On left thickness of subsets in semigroups

Wong, James C. S.

doi:10.1090/S0002-9939-1982-0640241-0

On left thickness of subsets in semigroups
HTML articles powered by AMS MathViewer

by James C. S. Wong PDF

Proc. Amer. Math. Soc. 84 (1982), 403-407 Request permission

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

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

Abstract harmonic analysis

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