Results 131 to 140 of about 199 (164)
Some of the next articles are maybe not open access.
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
openaire +1 more source
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
openaire +1 more source
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.
openaire +1 more source
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.
openaire +1 more source
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.
openaire +2 more sources
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.
openaire +2 more sources
On the fuzzy Hahn–Banach Theorem – an analytic form
Fuzzy Sets and Systems, 1999The authors investigate the relation between fuzzy seminorms and crisp seminorms on a linear space \(X\), and fuzzify the analytic form of the Hahn-Banach theorem.
Gil-Seob Rhie, In-Ah Hwang
openaire +1 more source
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 =
openaire +1 more source
Borel complexity and computability of the Hahn–Banach Theorem
Archive for Mathematical Logic, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
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.
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
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.
openaire +1 more source
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 ...
openaire +1 more source