Smooth Norms that Depend Locally on Finitely many Coordinates

DOI10.2307/2161911zbMath0853.46010OpenAlexW4253112214MaRDI QIDQ4874280

Petr Hájek

Publication date: 21 April 1996

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2161911

zbMATH Keywords

separable normed spacesequivalent \(C^ \infty\)-smooth normsnormed space with countable algebraic basis

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Local theory of Banach spaces (46B07) Isomorphic theory (including renorming) of Banach spaces (46B03) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Duality and reflexivity in normed linear and Banach spaces (46B10)

Related Items (21)

Analytic norms in Orlicz spaces ⋮ LFC bumps on separable Banach spaces ⋮ Using boundaries to find smooth norms ⋮ Smooth and polyhedral approximation in Banach spaces ⋮ Polyhedrality in pieces ⋮ On a problem of H.\,P.\ Rosenthal concerning operators on \(C\)[0,1] ⋮ A note on bump functions that locally depend on finitely many coordinates ⋮ Smoothing of bump functions ⋮ Renormings of \(C(K)\) spaces ⋮ Extraction of critical points of smooth functions on Banach spaces ⋮ Some remarks on smooth renormings of Banach spaces ⋮ Limits of sequences of continuous functions depending on finitely many coordinates ⋮ Polyhedrality in Orlicz spaces ⋮ Locally flat Banach spaces ⋮ Asymptotic structure, \(\ell_p\)-estimates of sequences, and compactness of multilinear mappings ⋮ Analytic and polyhedral approximation of convex bodies in separable polyhedral Banach spaces ⋮ Smooth norms in dense subspaces of Banach spaces ⋮ Topology, isomorphic smoothness and polyhedrality in Banach spaces ⋮ On densely isomorphic normed spaces ⋮ A note on extreme points of $C^\infty $-smooth balls in polyhedral spaces ⋮ On Preserved and Unpreserved Extreme Points

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