Results 121 to 130 of about 199 (164)
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Resonance, 2017
The Hahn–Banach theorem is one of the major theorems proved in any first course on functional analysis. It has plenty of applications, not only within the subject itself, but also in other areas of mathematics like optimization, partial differential equations, and so on.
S Kesavan, Kesavan S
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The Hahn–Banach theorem is one of the major theorems proved in any first course on functional analysis. It has plenty of applications, not only within the subject itself, but also in other areas of mathematics like optimization, partial differential equations, and so on.
S Kesavan, Kesavan S
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The Hahn–Banach–Lagrange theorem
Optimization, 2007This article is about a new version of the Hahn–Banach theorem, which we will call the “Hahn–Banach–Lagrange theorem”, since it deals very effectively with certain problems of Lagrange type, as well as giving numerous results in functional analysis, convex analysis, and monotone operator theory. We will discuss several of these results in this article.
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On the Constructive Hahn-Banach Theorem
Bulletin of the London Mathematical Society, 1989We prove that if we confine ourselves to some classes of normed linear spaces, then the exact existence of the extensions of a linear functional is constructively provable.
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2007
A fuzzy version of the Hahn-Banach theorem is proved based on the classical result. A comparison is also drawn with an earlier published result in this connection.
Wesley Kotzé, Andrew L. Pinchuck
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A fuzzy version of the Hahn-Banach theorem is proved based on the classical result. A comparison is also drawn with an earlier published result in this connection.
Wesley Kotzé, Andrew L. Pinchuck
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2020
The Hahn–Banach theorem is another fundamental principle of functional analysis, which allows extending continuous linear functionals on a subspace while preserving continuity and linearity. An alternative version allows the separation of convex sets by hyperplanes. This chapter covers both versions together with their most important consequences.
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The Hahn–Banach theorem is another fundamental principle of functional analysis, which allows extending continuous linear functionals on a subspace while preserving continuity and linearity. An alternative version allows the separation of convex sets by hyperplanes. This chapter covers both versions together with their most important consequences.
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Hahn–Banach theorems for MV-algebras
Soft Computing, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1972
We shall now discuss the Hahn-Banach Theorem, which is the basic tool in the subsequent analysis. We shall not present proofs of the theorems, since they can be found in the extensive literature on functional analysis.
Igor Vladimirovich Girsanov +1 more
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We shall now discuss the Hahn-Banach Theorem, which is the basic tool in the subsequent analysis. We shall not present proofs of the theorems, since they can be found in the extensive literature on functional analysis.
Igor Vladimirovich Girsanov +1 more
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1977
Many of the important applications of the theory of topological linear spaces concern the relations between a space ℰ and the space of continuous linear functionals on ℰ. This space is known as the conjugate space or dual space of ℰ and will be denoted by ℰ* in the sequel. (When ℰ is a normed space, ℰ* = ℒ(ℰ, ℂ) is a Banach space (Prop.
Arlen Brown, Carl Pearcy
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Many of the important applications of the theory of topological linear spaces concern the relations between a space ℰ and the space of continuous linear functionals on ℰ. This space is known as the conjugate space or dual space of ℰ and will be denoted by ℰ* in the sequel. (When ℰ is a normed space, ℰ* = ℒ(ℰ, ℂ) is a Banach space (Prop.
Arlen Brown, Carl Pearcy
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1965
In a Hilbert space, we can introduce the notion of orthogonal coordinates through an orthogonal base, and these coordinates are the values of bounded linear functionals defined by the vectors of the base. This suggests that we consider continuous linear functionals, in a linear topological space, as generalized coordinates of the space.
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In a Hilbert space, we can introduce the notion of orthogonal coordinates through an orthogonal base, and these coordinates are the values of bounded linear functionals defined by the vectors of the base. This suggests that we consider continuous linear functionals, in a linear topological space, as generalized coordinates of the space.
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2009
The analytic form of the Hahn-Banach theorem concerns the extension of linear functional defined on a subspace of a normed linear space to the entire space, preserving the norm of the functional. We will prove a slightly more general result in this direction.
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The analytic form of the Hahn-Banach theorem concerns the extension of linear functional defined on a subspace of a normed linear space to the entire space, preserving the norm of the functional. We will prove a slightly more general result in this direction.
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