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On the abstract Hahn-Banach theorem due to Rodé. (English) Zbl 0636.46005

G. Rodé [Arch. Math. 31, 474-481 (1978; Zbl 0402.46003)] proved a very abstract Hahn-Banach theorem. His proof is rather complicated. Here the author presents a simpler proof of it.
Reviewer: T.Husain

MSC:

46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators
52A40 Inequalities and extremum problems involving convexity in convex geometry
26B25 Convexity of real functions of several variables, generalizations
39B72 Systems of functional equations and inequalities

Citations:

Zbl 0402.46003
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References:

[1] Fuchssteiner, Benno andLusky, Wolfgang,Convex Cones. (North-Holland Mathematics Studies Vol. 56), Amsterdam–New York–Oxford, 1981.
[2] König, Heinz,Der Hahn-Banach-Satz von Rodé für unendlichstellige Operationen. Arch. Math.35 (1980), 292–304. · Zbl 0476.46004
[3] Kuhn, Norbert,A note on t-convex functions. In:General Inequalities 4 (Oberwolfach, 8–14 May 1983), (ISNM Vol. 71.) Birkhäuser, Basel–Boston–Stuttgart, 1984, pp. 269–276.
[4] Rodé, Gerd,Eine abstrakte Version des Satzes von Hahn-Banach. Arch. Math.31 (1978), 474–481. · Zbl 0402.46003
[5] Volkmann, Peter undWeigel, Herbert,Systeme von Funktionalgleichungen. Arch. Math.37 (1981), 443–449. · Zbl 0458.39004
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