The radius ratio and convexity properties in normed linear spaces

D. Amir; C. Franchetti

doi:10.1090/S0002-9947-1984-0728713-8

The radius ratio and convexity properties in normed linear spaces

D. Amir, C. Franchetti

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

The sup remum 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 ^-convexity, superreflexivity and P-convexity.

Original language	English
Pages (from-to)	275-291
Number of pages	17
Journal	Transactions of the American Mathematical Society
Volume	282
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9947-1984-0728713-8
State	Published - Mar 1984

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The radius ratio and convexity properties in normed linear spaces

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