The radius ratio and convexity properties in normed linear spaces

Author:

Amir D.,Franchetti C.

Abstract

The supremum of the ratios of the self-radius r A ( A ) {r_A}(A) of a convex bounded set in a normed linear space X X to its absolute radius r X ( A ) {r_X}(A) is related to the supremum of the relative projection constants of the maximal subspaces of X X . Necessary conditions and sufficient conditions for these suprema to be smaller than 2 are given. These conditions are selfadjoint superproperties similar to B B -convexity, superreflexivity and P P -convexity.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference25 articles.

1. On Jung’s constant and related constants in normed linear spaces;Amir, Dan;Pacific J. Math.,1985

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3. A convexity condition in Banach spaces and the strong law of large numbers;Beck, Anatole;Proc. Amer. Math. Soc.,1962

4. Convex regions and projections in Minkowski spaces;Bohnenblust, F.;Ann. of Math. (2),1938

5. Normal structure coefficients for Banach spaces;Bynum, W. L.;Pacific J. Math.,1980

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