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The radius ratio and convexity properties in normed linear spaces


Authors: D. Amir and C. Franchetti
Journal: Trans. Amer. Math. Soc. 282 (1984), 275-291
MSC: Primary 46B20; Secondary 41A65
DOI: https://doi.org/10.1090/S0002-9947-1984-0728713-8
MathSciNet review: 728713
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Abstract: The supremum of the ratios of the self-radius $ {r_A}(A)$ of a convex bounded set in a normed linear space $ X$ to its absolute radius $ {r_X}(A)$ is related to the supremum of the relative projection constants of the maximal subspaces of $ X$. Necessary conditions and sufficient conditions for these suprema to be smaller than 2 are given. These conditions are selfadjoint superproperties similar to $ B$-convexity, superreflexivity and $ P$-convexity.


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DOI: https://doi.org/10.1090/S0002-9947-1984-0728713-8
Article copyright: © Copyright 1984 American Mathematical Society

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