Results 61 to 70 of about 3,277 (79)
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The wigner property for CL-spaces and finite-dimensional polyhedral Banach spaces
Proceedings of the Edinburgh Mathematical Society, 2021AbstractWe say that a map $f$ from a Banach space $X$ to another Banach space $Y$ is a phase-isometry if the equality \[ \{\|f(x)+f(y)\|, \|f(x)-f(y)\|\}=\{\|x+y\|, \|x-y\|\} \]holds for all $x,\,y\in X$. A Banach space $X$ is said to have the Wigner property if for any Banach space $Y$ and every surjective phase-isometry $f : X\rightarrow Y$, there ...
Tan, Dongni, Huang, Xujian
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Massiveness of the set of extreme points of the dual ball of a Banach space. Polyhedral spaces
Functional Analysis and Its Applications, 1978openaire +3 more sources
Self-Conjugate Polyhedral Banach Spaces
Bulletin of the London Mathematical Society, 1986Problem 91 (of Mazur) in the Scottish Book asked whether a real finite- dimensional Banach space isometric to its dual is necessarily isometrically an inner-product space. Answering this in the negative, Sztencel and Zaremba asked whether self-conjugate normed spaces with polyhedral unit balls exist for dimensions \(n\geq 3.\) An affirmative answer to ...
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Operations Research Letters, 2020
This article studies the containment problem of a polyhedral set in a Banach space. The first two sections present the background definitions and preliminary results on set containment problems and dual characterizations, followed by a presentation of the dual characterization of set containments defined by lower semicontinuous and sublinear functions.
Hedayat, A., Mohebi, H.
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This article studies the containment problem of a polyhedral set in a Banach space. The first two sections present the background definitions and preliminary results on set containment problems and dual characterizations, followed by a presentation of the dual characterization of set containments defined by lower semicontinuous and sublinear functions.
Hedayat, A., Mohebi, H.
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Extreme points in polyhedral Banach spaces
Israel Journal of Mathematics, 2017Polyhedral Banach spaces were introduced by \textit{V. Klee} at the end of the paper [Acta Math. 103, 243--267 (1960; Zbl 0148.16203)] in 1960 as those real spaces where the unit balls of all subspaces are polygons. \(c_0\) serves as the basic example of such a space, and Klee proved in the last theorem of that paper the non-trivial fact that \(c_0 ...
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Approximation by Polyhedral $G$ Chains in Banach Spaces
Zeitschrift für Analysis und ihre Anwendungen, 2014In a Banach space with the metric approximation property, each compactly supported rectifiable G chain whose boundary is rectifiable as well, is approximatable in the flat norm by a polyhedral G
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Isomorphically Polyhedral Banach Spaces
2016We prove two theorems giving su??cient conditions for a Banach space to be isomorphically polyhedral.
Fonf, V.P. +2 more
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An algorithm for the best approximation by elements of a polyhedral set in banach spaces
Numerical Functional Analysis and Optimization, 1983The purpose of this paper is to give an algorithm for finding the best approximation by elements of a polyhedral set of a reflexive and strictly convex Banach space. A dual problem is defined whose solutions can be used to find the solution of the initial one.
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Proximinality Properties in Lp(μ, X) and Polyhedral Direct Sums of Banach Spaces
Numerical Functional Analysis and Optimization, 2014For a closed subspace Y of a Banach space X, we define a separably determined property for Y in X. We prove that if the strong -ball property is separably determined for Y in X, then L 1(μ, Y) has the strong -ball property in L 1(μ, X). For an M-embedded space X, we give a class of elements in L 1(μ, X **) having best approximations from L 1(μ, X).
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