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$k$-smoothness on polyhedral Banach spaces [PDF]
Colloquium Mathematicum, 2022 11 ...
Dey, Subhrajit +2 more
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Smooth and polyhedral approximation in Banach spaces
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.
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Structure of Pareto Solutions of Generalized Polyhedral-Valued Vector Optimization Problems in Banach Spaces [PDF]
Abstract and Applied Analysis, 2013 In general Banach spaces, we consider a vector optimization problem (SVOP) in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra or the union of finitely many generalized polyhedra.
Qinghai He, Weili Kong
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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 ...
Debmalya Sain +3 more
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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 ∗ {X^\ast } is an L-space this condition is also necessary.
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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Generic orbits and type isolation in the Gurarij space [PDF]
, 2016 We study the question of when the space of embeddings of a separable Banach space $E$ into the separable Gurarij space $\mathbf G$ admits a generic orbit under the action of the linear isometry group of $\mathbf G$.
Henson, C. Ward, Yaacov, Itaï Ben
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Intersection Properties of Balls in Banach Spaces
Journal of Function Spaces and Applications, 2013 We introduce a weaker notion of central subspace called almost central subspace, and we study Banach spaces that belong to the class (GC), introduced by Veselý (1997). In particular, we prove that if is an almost central subspace of a Banach space such
C. R. Jayanarayanan
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A ``hidden'' characterization of approximatively polyhedral convex sets in Banach spaces [PDF]
Studia Mathematica, 2012 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 is a polyhedral convex subset $P\subset X$ on Hausdorff distance $d_H(P,C)0$ (resp.
Banakh, Taras, Hetman, Ivan
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Almost minimal orthogonal projections
, 2020 The projection constant $\Pi(E):=\Pi(E, \ell_\infty)$ of a finite-dimensional Banach space $E\subset\ell_\infty$ is by definition the smallest norm of a linear projection of $\ell_\infty$ onto $E$. Fix $n\geq 1$ and denote by $\Pi_n$ the maximal value of
Basso, Giuliano
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