Analytic and polyhedral approximation of convex bodies in separable polyhedral Banach spaces
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Publication:1264280
DOI10.1007/BF02780326zbMath0920.46011OpenAlexW2030193462MaRDI QIDQ1264280
Robert Deville, Petr Hájek, Vladimir P. Fonf
Publication date: 1 September 1998
Published in: Israel Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02780326
Geometry and structure of normed linear spaces (46B20) Isomorphic theory (including renorming) of Banach spaces (46B03) Convex sets in topological vector spaces (aspects of convex geometry) (52A07)
Related Items (28)
Analytic norms in Orlicz spaces ⋮ Every closed convex set is the set of minimizers of some $C^{\infty }$-smooth convex function ⋮ Perturbed smooth Lipschitz extensions of uniformly continuous functions on Banach spaces ⋮ Using boundaries to find smooth norms ⋮ Boundaries and polyhedral Banach spaces ⋮ Renormings preserving local geometry at countably many points in spheres of Banach spaces and applications ⋮ Smooth and polyhedral approximation in Banach spaces ⋮ Real analytic approximation of Lipschitz functions on Hilbert space and other Banach spaces ⋮ Gâteaux differentiability of bump functions in Banach spaces ⋮ Polyhedrality in pieces ⋮ Approximation of norms on Banach spaces ⋮ Polyhedral norms on non-separable Banach spaces ⋮ 𝐶^{𝑘}-smooth approximations of LUR norms ⋮ The Banach space of quasinorms on a finite-dimensional space ⋮ The Szlenk index of L p (X ) ⋮ Analytic approximations of uniformly continuous functions in real Banach spaces ⋮ Almost flat locally finite coverings of the sphere ⋮ Some remarks on smooth renormings of Banach spaces ⋮ On \(\omega \)-limit sets of ordinary differential equations in Banach spaces ⋮ On isomorphically polyhedral \(\mathcal{L}_\infty\)-spaces ⋮ Asymptotic structure, \(\ell_p\)-estimates of sequences, and compactness of multilinear mappings ⋮ Geometry of Banach spaces with property \(\beta\) ⋮ Smooth norms in dense subspaces of Banach spaces ⋮ Analytic approximation on \(c_0\) ⋮ Approximation of Lipschitz functions by \(\Delta\)-convex functions in Banach spaces ⋮ Smooth approximations without critical points of continuous mappings between Banach spaces, and diffeomorphic extractions of sets ⋮ Antiproximinal norms in Banach spaces ⋮ Smooth bump functions and the geometry of Banach spaces. A brief survey
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- Smooth Norms that Depend Locally on Finitely many Coordinates
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