Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Packing and reflexivity in Banach spaces

Author: Clifford A. Kottman
Journal: Trans. Amer. Math. Soc. 150 (1970), 565-576
MSC: Primary 46.10
MathSciNet review: 0265918
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Abstract: A measure of the ``massiveness'' of the unit ball of a Banach space is introduced in terms of an efficiency of the tightest packing of balls of equal size in the unit ball. This measure is computed for the $ {l_p}$-spaces, and spaces with distinct measures are shown to be not nearly isometric. A new convexity condition, which is compared to $ B$-convexity, uniform smoothness, and uniform convexity, is introduced in terms of this measure, and is shown to be a criterion of reflexivity. The property dual to this convexity condition is also exposed and examined.

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Keywords: Packing, reflexivity, nearly isometric spaces, $ B$-convexity, $ P$-convexity, uniformly smooth, uniformly convex, geometry of the unit ball
Article copyright: © Copyright 1970 American Mathematical Society