Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order

Du\v{s}an Repov\v{s}; Maxim V. Balashov

arxiv: 1101.5685 · v1 · pith:KF54GHMRnew · submitted 2011-01-29 · 🧮 math.FA · math.GN

Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order

Maxim V. Balashov , Du\v{s}an Repov\v{s} This is my paper

classification 🧮 math.FA math.GN

keywords convexconvexityhilbertmodulusorderradiussecondspace

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We prove that in the Hilbert space every uniformly convex set with modulus of convexity of the second order at zero is an intersection of closed balls of fixed radius. We also obtain an estimate of this radius.

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Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order

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