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Amenable transformation semigroups

Published online by Cambridge University Press:  09 April 2009

Carroll Wilde  and
Toke Jayachandran
Carroll Wilde
Affiliation:
Naval Postgraduate School Monterey
Toke Jayachandran
Affiliation:
Naval Postgraduate School Monterey
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For any set X denote by m(X) the Banach space of all bounded real-valued functions on X, equipped with the supremum norm, and denote by (X) the semigroup (under functional composition) of all transformations of X, i.e. mappings with domain X and range contained in X. A pair (X, S), where S is a subsernigroup of (X), will be called a transformation semigroup. Important examples are obtained by letting X be the underlying set in an abstract semigroup and considering the pairs (X, S1) and (X, S2), where S1 [Sn] denotes the set of left [right] multiplication mappings of X. We shall call transformation semigroups in these classes of examples l-[r-] semigroups.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 4 , November 1971 , pp. 502 - 510
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Day, M. M., ‘Amenable semigroups’, Ill. J. Math. 1 (1957), 509–544.Google Scholar
[2]Day, M. M., ‘Fixed point theorems for compact convex sets’, Ill. J. Math. 5 (1961), 585–590.Google Scholar
[3]Day, M. M., ‘Semigroups and amenability’, to appear in the at Proceedings of a Symposium on SemigroupsWayne State University,June 1968, Academic Press.Google Scholar
[4]Granirer, E., ‘Extremely amenable semigroups I’, Math. Scand. 17 (1965), 177–197.CrossRefGoogle Scholar
[5]Granirer, E., ‘Extremely amenable semigroups II’, Math. Scand. 20 (1967), 93–113.CrossRefGoogle Scholar
[6]Granirer, E., ‘Extremely amenable semigroups III’, to appear.Google Scholar
[7]Hewitt, E. and Ross, K., Abstract Harmonic Analysis, Vol. 1. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963.Google Scholar
[8]Mitchell, T., ‘Fixed points and multiplicative left invariant means’, Trans. Amer. Math. Soc. 122 (1966), 195–202.CrossRefGoogle Scholar
[9]Namioka, I., ‘Følner's condition for amenable semigroups’, Math. Scand. 15 (1964), 18–28.CrossRefGoogle Scholar
[10]Rosen, W. G., ‘On invariant means over compact semigroups’, Proc. Amer. Math. Soc. 7 (1956), 1076–1082.CrossRefGoogle Scholar
[11]Wilde, C. and Witz, K., ‘Invariant means and the Stone-Ĉech compactification’, Pac. J. Math. 21 (1967), 577–586.CrossRefGoogle Scholar