Functional analytic properties of extremely amenable semigroups

Functional analytic properties of extremely amenable semigroups
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Trans. Amer. Math. Soc. 137 (1969), 53-75

DOI: https://doi.org/10.1090/S0002-9947-1969-0239408-3

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References

F. F. Bonsall, J. Lindenstrauss, and R. R. Phelps, Extreme positive operators on algebras of functions, Math. Scand. 18 (1966), 161–182. MR 209863, DOI 10.7146/math.scand.a-10789
Mahlon M. Day, Normed linear spaces, Reihe: Reelle Funktionen, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. MR 0094675
Mahlon M. Day, Means for the bounded functions and ergodicity of the bounded representations of semi-groups, Trans. Amer. Math. Soc. 69 (1950), 276–291. MR 44031, DOI 10.1090/S0002-9947-1950-0044031-5
Mahlon M. Day, Amenable semigroups, Illinois J. Math. 1 (1957), 509–544. MR 92128
Mahlon M. Day, Fixed-point theorems for compact convex sets, Illinois J. Math. 5 (1961), 585–590. MR 138100
Jacques Dixmier, Les moyennes invariantes dans les semi-groupes et leurs applications, Acta Sci. Math. (Szeged) 12 (1950), 213–227 (French). MR 37470

Linear operators

Erling Følner, Generalization of a theorem of Bogolioùboff to topological abelian groups. With an appendix on Banach mean values in non-abelian groups, Math. Scand. 2 (1954), 5–18. MR 64062, DOI 10.7146/math.scand.a-10389
Erling Følner, On groups with full Banach mean value, Math. Scand. 3 (1955), 243–254. MR 79220, DOI 10.7146/math.scand.a-10442
Erling Følner, Note on groups with and without full Banach mean value, Math. Scand. 5 (1957), 5–11. MR 94725, DOI 10.7146/math.scand.a-10482

Studies in amenable semigroups

I. Gelfand, D. Raikov, and G. Shilov, Commutative normed rings, Chelsea Publishing Co., New York, 1964. Translated from the Russian, with a supplementary chapter. MR 0205105
E. Granirer, On amenable semigroups with a finite-dimensional set of invariant means. I, Illinois J. Math. 7 (1963), 32–48. MR 144197
Edmond Granirer, A theorem on amenable semigroups, Trans. Amer. Math. Soc. 111 (1964), 367–379. MR 166597, DOI 10.1090/S0002-9947-1964-0166597-7
E. Granirer, Extremely amenable semigroups, Math. Scand. 17 (1965), 177–197. MR 197595, DOI 10.7146/math.scand.a-10772
E. Granirer, Extremely amenable semigroups. II, Math. Scand. 20 (1967), 93–113. MR 212551, DOI 10.7146/math.scand.a-10825
E. E. Granirer, On the range of an invariant mean, Trans. Amer. Math. Soc. 125 (1966), 384–394. MR 204551, DOI 10.1090/S0002-9947-1966-0204551-9

Abstract harmonic analysis

E. S. Ljapin, Semigroups, Translations of Mathematical Monographs, Vol. 3, American Mathematical Society, Providence, R.I., 1963. MR 0167545, DOI 10.1090/mmono/003
Lynn H. Loomis, An introduction to abstract harmonic analysis, D. Van Nostrand Co., Inc., Toronto-New York-London, 1953. MR 0054173
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, Fixed points and multiplicative left invariant means, Trans. Amer. Math. Soc. 122 (1966), 195–202. MR 190249, DOI 10.1090/S0002-9947-1966-0190249-2
I. Namioka, Følner’s conditions for amenable semi-groups, Math. Scand. 15 (1964), 18–28. MR 180832, DOI 10.7146/math.scand.a-10723
R. J. Silverman, Invariant means and cones with vector interiors, Trans. Amer. Math. Soc. 88 (1958), 75–79. MR 95414, DOI 10.1090/S0002-9947-1958-0095414-6

Existence of measures that are invariant under a semigroup of transformations

Carroll Wilde and Klaus Witz, Invariant means and the Stone-Čech compactification, Pacific J. Math. 21 (1967), 577–586. MR 212552, DOI 10.2140/pjm.1967.21.577
Klaus G. Witz, Applications of a compactification for bounded operator semigroups, Illinois J. Math. 8 (1964), 685–696. MR 178368
John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
E. Kamke, Theory of Sets. Translated by Frederick Bagemihl, Dover Publications, Inc., New York, N.Y., 1950. MR 0032709
I. Glicksberg, On convex hulls of translates, Pacific J. Math. 13 (1963), 97–113. MR 151860, DOI 10.2140/pjm.1963.13.97