Results 111 to 120 of about 854 (144)

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.
C Zălinescu
exaly   +2 more sources

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 ...
Boris Lavrič
openaire   +3 more sources

The Hahn–Banach theorem almost everywhere [PDF]

Aequationes Mathematicae, 2015
The aim of this work is to present an almost everywhere version of the Hahn– Banach extension ...
Roman Badora
exaly   +2 more sources

The Hahn-Banach theorem: the life and times

Topology and Its Applications, 1997
Without the Hahn-Banach theorem, functional analysis would be very different from the structure we know today. Among other things, it has proved to be a very appropriate form of the Axiom of Choice for the analyst.
Edward Beckenstein
exaly   +2 more sources

How Incomputable is the Separable Hahn-Banach Theorem?

Electronic Notes in Theoretical Computer Science, 2008
We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis.
Guido Gherardi, Alberto Marcone
exaly   +2 more sources

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
openaire   +2 more sources

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
openaire   +1 more source

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
openaire   +3 more sources

An n-Dimensional Hahn-Banach Extension Theorem and Minimal Projections

Journal of Computational Analysis and Applications, 2003
Let \(Z\) be a Banach space and let \(\mathbb F\) be the underlying real or complex field. If \(z\in Z\) and \(z^\ast\in Z^\ast\) are such that \(\langle z,z^\ast\rangle=\| z\| \,\| z^\ast\| \not=0\), then \(z^\ast\) is said to be an extremal for \(z\) and one writes \(z^\ast=\text{ext}(z)\).
openaire   +1 more source

Hahn-Banach extension theorems over the space of fuzzy elements

Fuzzy Optimization and Decision Making, 2010
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openaire   +2 more sources