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A characterization of \(\sigma\)-extremely amenable semitopological semigroups. (English) Zbl 1460.43001

The author studies and characterizes a twisted notion of left amenability for left semitopological algebras in terms of a nonlinear property which is a generalization of some classical results. Some results for amenability of Banach algebras are also given.

MSC:

43A07 Means on groups, semigroups, etc.; amenable groups
22A15 Structure of topological semigroups
46H10 Ideals and subalgebras
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)

Citations:

Zbl 0219.22003
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References:

[1] J. F. Berglund, H. D. Junghenn and P. Milnes,Analysis on Semigroups, John Wiley & Sons, New York, 1989. · Zbl 0727.22001
[2] A. Bowers and N. J. Kalton,An Introductory Course in Functional Analysis, Springer 2014. · Zbl 1328.46001
[3] E. Granirer,Extremely amenable semigroups, Math. Scand.17(1965), 177-197. · Zbl 0136.27202
[4] E. Granirer,Extremely amenable semigroups II, Math. Scand.20(1967), 93-113. · Zbl 0204.03501
[5] E. Granirer,On invariant mean on topological semigroups and on topological groupsPacific J. Math.15(1965), 107-140. · Zbl 0144.38203
[6] E. Granirer and A. T. Lau,Invariant means on locally compact groups, Illinois J. Math.15 (1971), 249-257. · Zbl 0212.14904
[7] E. Hewitt,On two problems of Urysohn, Ann. Math.47(1946), 503-509. · Zbl 0060.39511
[8] G. Itzkowitz and T. Mitchell,Topological semigroups and fixed points II, Notices Amer. Math. Soc.13(1966), 725.
[9] A. T.-M. Lau,Topological semigroups with invariant means in the convex hull of multiplicative means, Trans. Amer. Math. Soc.148(1970), 69-84. · Zbl 0201.02901
[10] A. T.-M. Lau, Invariant means on almost periodic functions and fixed point properties, Rocky Mountain J. Math.3(1973), 69-76. · Zbl 0279.43002
[11] A. T.-M. Lau and Y. Zhang,Fixed point properties for semigroups of nonlinear mappings and amenability, J. Funct. Anal.263(2012), 2949-2977. · Zbl 1275.47115
[12] P. Milnes and J. S. Pym,Function spaces on semitopological semigroups, Semigroup forum. 19(1980), 347-354. · Zbl 0452.43003
[13] T. Mitchell,Fixed points and multiplicative left invariant means, Trans. Amer. Math. Soc.122 (1966), 195-202. · Zbl 0146.12101
[14] T. Mitchell,Topological semigroups and fixed points, Illinois J. Math.14(1970), 630-641. · Zbl 0219.22003
[15] I.
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