Results 11 to 20 of about 75,695 (101)
Smooth and polyhedral approximation in Banach spaces [PDF]
Journal of Mathematical Analysis and Applications, 2015 We show that norms on certain Banach spaces $X$ can be approximated uniformly, and with arbitrary precision, on bounded subsets of $X$ by $C^{\infty}$ smooth norms and polyhedral norms.
Bible, Victor, Smith, Richard J.
core +4 more sources
Polyhedral direct sums of Banach spaces, and generalized centers of finite sets
Journal of Mathematical Analysis and Applications, 2012 Let \(X\) be a real Banach space. \(X\) is said to satisfy \((GC)\) if for every \(n\) and for every real-valued continuous, nondecreasing coercive function \(f\) on \( [0,\infty)^n\), the set \(E_f(a)\) of minimizers of the function \(\phi(x) = f(\|x-a_1\|,\dots,\|x-a_n\|)\) is nonempty, where \(x \in X\) and \(a= (a_1,\dots,a_n) \in X^n\).
L. Veselý
semanticscholar +4 more sources
Unit balls of polyhedral Banach spaces with many extreme points [PDF]
Studia Mathematica, 2023 Let $E$ be a $(\mathrm{IV})$-polyhedral Banach space. We show that, for each $\epsilon>0$, $E$ admits an $\epsilon$-equivalent $\mathrm{(V)}$-polyhedral norm such that the corresponding closed unit ball is the closed convex hull of its extreme points. In
C. D. Bernardi
semanticscholar +5 more sources
$k$-smoothness on polyhedral Banach spaces [PDF]
Colloquium Mathematicum, 2020 We characterize $k-$smoothness of an element on the unit sphere of a finite-dimensional polyhedral Banach space. Then we study $k-$smoothness of an operator $T \in \mathbb{L}(\ell_{\infty}^n,\mathbb{Y}),$ where $\mathbb{Y}$ is a two-dimensional Banach ...
Subhrajit Dey, A. Mal, K. Paul
semanticscholar +4 more sources
On the numerical index of polyhedral Banach spaces [PDF]
Linear Algebra and its Applications, 2018 The computation of the numerical index of a Banach space is an intriguing problem, even in case of two-dimensional real polyhedral Banach spaces. In this article we present a general method to estimate the numerical index of any finite-dimensional real ...
D. Sain +3 more
semanticscholar +5 more sources
Boundaries and polyhedral Banach spaces [PDF]
Proceedings of the American Mathematical Society, 2014 We show that if X and Y are Banach spaces, where Y is separable and polyhedral, and if T : X → Y is a bounded linear operator such that T ∗(Y ∗) contains a boundary B of X, then X is separable and isomorphic to a polyhedral space.
V. Fonf, Richard J. Smith, S. Troyanski
semanticscholar +4 more sources
A note on polyhedral Banach spaces [PDF]
Proceedings of the American Mathematical Society, 1972 We give a sufficient condition for an infinitedimensional Banach space X to be polyhedral. If X ∗ {X^\ast } is an L-space this condition is also necessary.
A. Gleit, R. McGuigan
semanticscholar +3 more sources
Full length article: Best approximation in polyhedral Banach spaces
Journal of Approximation Theory, 2011 The authors study conditions under which the metric projection of a polyhedral Banach space \(X\) onto a closed subspace \(Y\) is Hausdorff lower or upper semicontinuous. The paper is organized as follows. Section 0 is an introduction. Section 1 contains notation concerning Banach spaces, followed by definitions and preliminary facts on polyhedral ...
V. Fonf, J. Lindenstrauss, L. Veselý
semanticscholar +2 more sources
A SUBSEQUENCE CHARACTERIZATION OF SEQUENCES SPANNING ISOMORPHICALLY POLYHEDRAL BANACH SPACES [PDF]
Studia Mathematica, 1996 Let (xn) be a sequence in a Banach space X which does not converge in norm, and let E be an isomorphically precisely norming set for X such that X n jx (xn+1 xn)j < 1; 8x 2 E: () Then there exists a subsequence of (xn) which spans an isomorphically ...
G. Androulakis
semanticscholar +5 more sources
A "hidden" characterization of approximatively polyhedral convex sets in Banach spaces [PDF]
Studia Mathematica, 2011 For a Banach space $X$ by $Conv_H(X)$ we denote the space of non-empty closed convex subsets of $X$, endowed with the Hausdorff metric. We prove that for any closed convex set $C\subset X$ and its metric component $H_C=\{A\in Conv_H(X):d_H(A,C) 0$ there ...
T. Banakh, I. Hetman
semanticscholar +4 more sources