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Hahn–Banach extension theorems for multifunctions revisited
Mathematical Methods of Operations Research, 2007Several 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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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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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 extension theorems
2002The 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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2014
In this chapter we present a generalization of the Hahn–Banach–Kantorovich extension theorem to K-convex set-valued maps, as well as Yang’s extension theorem. We also present classical separation theorems for convex sets, the core convex topology on a linear space, and a criterion for the convexity of the cone generated by a set.
Akhtar A. Khan +2 more
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In this chapter we present a generalization of the Hahn–Banach–Kantorovich extension theorem to K-convex set-valued maps, as well as Yang’s extension theorem. We also present classical separation theorems for convex sets, the core convex topology on a linear space, and a criterion for the convexity of the cone generated by a set.
Akhtar A. Khan +2 more
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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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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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2014
Several theorems in functional analysis have been labeled as “the Hahn–Banach Theorem.” At the heart of all of them is what we call here the Hahn–Banach Extension Theorem, given in Theorem 3.4, below. This theorem is at the foundation of modern functional analysis, and its use is so pervasive that its importance cannot be overstated.
Adam Bowers, Nigel J. Kalton
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Several theorems in functional analysis have been labeled as “the Hahn–Banach Theorem.” At the heart of all of them is what we call here the Hahn–Banach Extension Theorem, given in Theorem 3.4, below. This theorem is at the foundation of modern functional analysis, and its use is so pervasive that its importance cannot be overstated.
Adam Bowers, Nigel J. Kalton
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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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Hahn–Banach theorems for MV-algebras
Soft Computing, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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