The average distance property of classical Banach spaces II

Details The average distance property of classical Banach spaces II The average distance property of classical Banach spaces II

2002-02-11

arxiv.org/abs/math/0202093v1

Mathematics

Functional Analysis

10 pages, to appear in Bull. Austr. Math. Soc

Scientific paper

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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