What is the Hahn-Banach extension theorem?
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The Hahn-Banach extension theorem is a fundamental result in functional analysis that deals with the extension of linear functionals defined on a subspace of a normed linear space to the entire space while preserving the norm of the functional. The theorem has various generalizations and applications in different areas of mathematics. The analytic form of the theorem, as proven by Paz, provides a slightly more general result in this direction . Olteanu discusses the extension results for linear operators and their applications to isotonicity of convex operators on a convex cone, as well as the use of the Krein-Milman theorem in representation theory and Choquet theory . Gutev relates the Hahn-Banach extension property to pointwise Lipschitz approximations of semi-continuous functions in a general metric domain . Niculescu and Olteanu characterize the isotonicity of continuous convex functions on the positive cone using subdifferentials . Fernández y Fernández-Arroyo presents a simple and direct proof of the geometric version of the Hahn-Banach theorem in the real case .
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01 Dec 2020 | The paper provides a proof of the Hahn-Banach theorem, but it does not explicitly define or explain what the Hahn-Banach extension theorem is. |
| The paper does not provide information about the Hahn-Banach extension theorem. The paper is about the characterization of the isotonicity of convex functions and the generalization of the Hardy-Littlewood-Polya inequality. | |
5 Citations | The paper does not provide information about the Hahn-Banach extension theorem. |
6 Citations | The paper provides an overview of some Hahn-Banach type theorems, but does not explicitly state what the Hahn-Banach extension theorem is. |
| The paper provides an analytic form of the Hahn-Banach theorem, which concerns the extension of linear functionals from a subspace to the entire space while preserving the norm of the functional. |
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