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Hahn-Banach extension theorem for interval-valued functions and existence of quasilinear functionals

New Trends in Mathematical Science, 2018
Halise Levent, Yilmaz Yilmaz
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VALUATION EQUILIBRIUM AND PARETO OPTIMUM. [PDF]

Proc Natl Acad Sci U S A, 1954
Debreu G.
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Notes on Integration: IV. [PDF]

Proc Natl Acad Sci U S A, 1949
Stone MH.
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Linear Operations among Summable Functions. [PDF]

Proc Natl Acad Sci U S A, 1939
Dunford N, Pettis BJ.
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The Hahn-Banach Extension Theorem in Normed Linear Spaces over Topological Semifield

The Hahn-Banach Extension Theorem in Normed Linear Spaces over Topological Semifield
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Hahn–Banach extension theorems for multifunctions revisited

Mathematical Methods of Operations Research, 2007
Several generalizations of the Hahn-Banach extension theorem to \(K\)-convex multifunctions were stated recently. The author provides an easy direct proof for the multifunction version of the Hahn-Banach-Kantorovich theorem and shows that in a quite general situation it can be obtained from existing results.
Constantin Zalinescu
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Hahn-Banach extension theorems

2002
The Hahn-Banach problem for convergence vector spaces has its roots in classical functional analysis. Let E be a strict topological 𝓛F-space, M a vector subspace of E with the property that M ∩E n is closed in each E n - such a subspace is called stepwise closed. Further, let φ bea sequentially continuous linear functional on M.
R. Beattie, H.-P. Butzmann
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From the Hahn–Banach extension theorem to the isotonicity of convex functions and the majorization theory

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020
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Constantin P. Niculescu, Octav Olteanu
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U-algebras and the Hahn–Banach extension theorem

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1987
SynopsisAn Archimedean unital f-algebra A is called a U-algebra if, for every a∊A, there exists an invertible element u∊A such that a = u |a|. Characterisations of a U-algebra are established. As an application, an extension theorem of Hahn–Banach type on modules over a U-algebra and over the complexification of a Dedekind complete unital f-algebra is ...
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The Existence of Non-Trivial Bounded Functionals Implies the Hahn-Banach Extension Theorem

Zeitschrift für Analysis und ihre Anwendungen, 2001
We show that it is impossible to prove the existence of a linear (bounded or unbounded) functional on any L_\infty/C_0 without an uncountable form of the axiom of choice. Moreover, we show that if on each Banach space there exists at least one non-trivial bounded linear functional, then
Luxemburg, W. A. J., Väth, Martin
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