Invariant means on Banach spaces
Abstract
In this paper we study some generalization of invariant means on Banach spaces. We give some sufficient condition for the existence of the invariant mean and some examples where we have not it.
Keywords
invariant mean; amenable semigroup; Banach space
References
2. Bombal F., Vera G., Means in locally convex spaces and semireflexivity, Collect. Math. 24 (1973), 267–295 (in Spanish).
3. Gajda Z., Invariant means and representations of semigroups in the theory of functional equations, Wydawnictwo Uniwersytetu Śląskiego, Katowice, 1992.
4. Ger R., The singular case in the stability behavior of linear mappings, Grazer Math. Ber. 316 (1992), 59–70.
5. Godefroy G., Five lectures in Geometry of Banach spaces, Seminar on Functional Analysis (1987), 9–67.
6. Godefroy G., Kalton N.J., The ball topology and its application, Contemp. Math. 85 (1989), 195–237.
7. Greenleaf F.P., Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York–Toronto–London–Melbourne, 1969.
8. Hewitt E., Ross K., Abstract harmonic analysis. Vol. I, Academic Press, New York, 1962.
9. Rao T.S.S.R.K., L^1(µ,X) as a constrained subspace of its bidual, Proc. Indian Acad. Sci. Math. Sci. 109 (1999), no. 3, 309–315.
10. Székelyhidi L., A note on Hyers theorem, C. R. Math. Rep. Acad. Sci. Canada 8 (1986), 127–129.
11. Tabor J., Monomial selections of set-valued functions, Publicationes Math. Debrecen 56 (2000), no. 1–2, 33–42.
12. Tabor J., Note on reflexivity and invariant means, Univ. Iagel. Acta Math. 43 (2005), 99–102.
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