Results 51 to 60 of about 86 (68)
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Three characterizations of polyhedral Banach spaces
Ukrainian Mathematical Journal, 1990An infinite-dimensional Banach space E is called polyhedral, if intersections of all finite dimensional spaces with the unit ball are polyhedra. Three characterizations, up to isomorphism, of such spaces are given. A ``local'' characterization uses a normed set in the unit dual sphere.
V P Fonf, Fonf V P
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Analytic and polyhedral approximation of convex bodies in separable polyhedral Banach spaces
Israel Journal of Mathematics, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Petr Hajek +2 more
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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.
Hossein Mohebi, A Hedayat
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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.
Hossein Mohebi, A Hedayat
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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.
Constantin Zălinescu
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Pareto Solutions of Polyhedral-valued Vector Optimization Problems in Banach Spaces
Set-Valued and Variational Analysis, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xi Yin Zheng, Zheng Xi Yin
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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, 1978exaly +2 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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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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