Results 161 to 170 of about 513,304 (193)
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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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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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2009
The Hahn-Banach Theorem (H.B.T.) is called one of the three basic principles of linear analysis—the two others are the Uniform Boundedness Principle and the Open Mapping Theorem. We will study them in the next three lectures. The H.B.T. has several versions and several corollaries.
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The Hahn-Banach Theorem (H.B.T.) is called one of the three basic principles of linear analysis—the two others are the Uniform Boundedness Principle and the Open Mapping Theorem. We will study them in the next three lectures. The H.B.T. has several versions and several corollaries.
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Advanced Courses of Mathematical Analysis II, 2007
I love the Hahn-Banach theorem. I love it the way I love Casablanca and the Fontana di Trevi. It is something not so much to be read as fondled. What is “the Hahn-Banach theorem?” Let f be a continuous linear functional defined on a subspace M of a normed space X.
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I love the Hahn-Banach theorem. I love it the way I love Casablanca and the Fontana di Trevi. It is something not so much to be read as fondled. What is “the Hahn-Banach theorem?” Let f be a continuous linear functional defined on a subspace M of a normed space X.
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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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On some Theorems of Hahn, Banach and Steinhaus
Journal of the London Mathematical Society, 1953Erklärungen: Ist \(E\) ein normierter Vektorraum, so heißt \(E'\subset E\) ein \(\alpha\)-Teilraum von \(E\), wenn \(E' = \cup_1^\infty E_n\) ist und die Mengenfolge \(\{E_n\}\) die beiden Eigenschaften aufweist: 1. \(E_n\) in \(E\) nirgends dicht; 2. \(0\in E_1\); aus \(x,y\in E_n\) folgt \(x+y, x-y\in E_{n+1}\). \(E\) heißt \(\alpha\)-Raum, wenn \(E =
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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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On the Hahn-Banach theorem for groups
Archiv der Mathematik, 2006Let \( \mathcal{G} \) be the family of all groups such that under each subadditive functional there exists an additive functional. We show that the class \( \mathcal{G} \) is between the class of all amenable groups and the family of all groups for which the Hyers stability theorem for homomorphisms holds true.
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Results with the Hahn-Banach Theorem
1997This chapter is devoted to several results the proofs of which are based on a theorem known as the Hahn-Banach theorem (due to H. Hahn, 1927, and S. Banach, 1929). Most of these results, as well as the Hahn-Banach theorem itself, are extension theorems dealing with extension of a (linear) operator from a linear subspace to the entire space, thereby ...
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A Generalization of the Hahn-Banach Theorem
Journal of the London Mathematical Society, 1965openaire +2 more sources