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The average distance property of classical Banach spaces II

Aicke Hinrichs·J. Wenzel
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Abstract

A Banach space X has the average distance property (ADP) if there exists a unique real number r such that for each positive integer n and all x_1,...,x_n in the unit sphere of X there is some x in the unit sphere of X such that 1/n \sum_{k=1}^n ||x_k-x|| = r. We show that l_p does not have the average distance property if p>2. This completes the study of the ADP for l_p spaces.

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Aicke Hinrichs, J. Wenzel. 2002-02-11. The average distance property of classical Banach spaces II. https://arxiv.org/abs/math/0202093

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