Results 1 to 10 of about 89 (74)
$k$-smoothness on polyhedral Banach spaces [PDF]
Colloquium Mathematicum, 2022 11 ...
Arpita Mal, Kallol Paul
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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 ...
Libor Vesely +2 more
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On the numerical index of polyhedral Banach spaces [PDF]
Linear Algebra and Its Applications, 2019 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 polyhedral Banach space, by considering the action of only finitely many functionals, on the unit ...
Kallol Paul +2 more
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Smooth and polyhedral approximation in Banach spaces
Journal of Mathematical Analysis and Applications, 2016 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. In particular, we show that this holds for any equivalent norm on $c_0(Γ)$, where $Γ$ is an arbitrary set.
Bible, Victor, Smith, Richard J.
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Polyhedral norms on non-separable Banach spaces
Journal of Functional Analysis, 2008 A Banach space \(X\) is called polyhedral if the unit ball of each of its finite-dimensional subspaces is a polytope. Separable polyhedral spaces were investigated in detail; see, e.g., [\textit{V. P. Fonf, J.\,Lindenstrauss} and \textit{R. P. Phelps}, in: Handbook of the Geometry of Banach spaces, Vol.\ I, Elsevier, 599--670 (2001; Zbl 1086.46004 ...
S Troyanski
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Extension of isometries between unit spheres of finite-dimensional polyhedral Banach spaces
Journal of Mathematical Analysis and Applications, 2012 We prove that an onto isometry between unit spheres of finite-dimensional polyhedral Banach spaces extends to a linear isometry of the corresponding spaces.
Vladimir Kadets, MIGUEL Martin
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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 \(a= (a_1,\dots,a_n) \in X^n\).
Libor Vesely
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Unit balls of polyhedral Banach spaces with many extreme points
Studia MathematicaLet $E$ be a $(\mathrm{IV})$-polyhedral Banach space. We show that, for each $ε>0$, $E$ admits an $ε$-equivalent $\mathrm{(V)}$-polyhedral norm such that the corresponding closed unit ball is the closed convex hull of its extreme points. In particular, we obtain that every separable isomorphically polyhedral Banach space, for each $ε>0$, admits ...
Carlo Alberto De Bernardi
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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
Gleit, Alan, McGuigan, Robert
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Boundaries and polyhedral Banach spaces [PDF]
Proceedings of the American Mathematical Society, 2015 We show that if X X and Y Y are Banach spaces, where Y Y is separable and polyhedral, and if T : X → Y T:X\to Y is a bounded linear operator such that T ∗ ( Y ∗ )
Fonf, V. P., Smith, R. J., Troyanski, S.
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