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- W4361303757 abstract "We develop tools to produce equivalent norms with specific local geometry around infinitely many points in the sphere of a Banach space via an inductive procedure. We combine this process with smoothness results and techniques to solve two open problems posed in the recently published monograph [7] by A. J. Guirao, V. Montesinos and V. Zizler. Specifically, on the one hand we construct in every separable Banach space admitting a Ck-smooth norm an equivalent norm which is Ck-smooth but fails to be uniformly Gâteaux in any direction; and on the other hand we produce in c0(Γ) for any infinite Γ a C∞-smooth norm whose ball is dentable but whose sphere lacks any extreme points." @default.
- W4361303757 created "2023-03-31" @default.
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- W4361303757 date "2023-10-01" @default.
- W4361303757 modified "2023-09-27" @default.
- W4361303757 title "Renormings preserving local geometry at countably many points in spheres of Banach spaces and applications" @default.
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- W4361303757 doi "https://doi.org/10.1016/j.jmaa.2023.127276" @default.
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