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Proceedings of the IX Conference "Applications of algebra" (9 ; 07-13.03.2005 ; Zakopane, Poland)
Języki publikacji
Abstrakty
Let X be a real locally convex linear topological space. A functional f : X → lR is called sublinear provided that f is subadditive and f(nx) = nf(x),x ∈ X,n ∈ IN. We establish a one-to-one correspondence between the collectron of all sublinear functional satisfying some mild regularity conditions and the family of all nonempty convex and weakly"- compact subsets of the dual space X*.
Słowa kluczowe
Rocznik
Tom
Strony
67--76
Opis fizyczny
Bibliogr. 8 poz.
Twórcy
autor
- Institute of Mathematics and Computer Science Jan Długosz University of Częstochowa, al. Armii Krajowej 13/15, 42-200 Częstochowa, Poland
Bibliografia
- [1] E. Berz. Sublinear functions on IR. Aequationes Math., 12, pp. 200- 206, 1975.
- [2] J.P.R. Christensen. Topology and Borel structure. North Holland, Aamsterdam & American Elsevier, New York, 1984.
- [3] P. Fischer, Z. Słodkowski. Christensen zero sets and measurable convex functions. Proc. Amer. Math, Soc., 79, pp. 449-453, 1980.
- [4] R. Ger. Sublinear functionals and weak*-compactness. Talk presented at the 36-th Int. Symp. on Functional Equations, May 24 -30, 1998, Brno (Czech Republic); Report of Meeting: Aequationes Math., 56, p. 289, 1998.
- [5] R. Ger, B. Koclęga. Isometries and a generalized Cauchy equation. Aequationes Math., 60, pp. 72-79, 2000.
- [6] Z. Kominek. Convex functions in linear spaces. Prace Naukowe Uniwersytetu Śląskiego w Katowicach, nr 1087, Katowice, 1989.
- [7] M. Kuczma. An Introduciion to the Theory of Functional Equations and Inequalities. Cauchy's Equation and Jensen's Inequality, PWN & Uniwersytet Śląski, Warszawa-Kraków-Katowice, 1985.
- [8] K. Yosida. Functional Analysis, Sixth Edition, Springer-Verlag, Berlin-Heidelberg-New York, 1980.
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Bibliografia
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