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The average distance property of classical Banach spaces II

Published online by Cambridge University Press:  17 April 2009

Aicke Hinrichs
Affiliation:
Mathematisches Institut, FSU Jena, D-07743 Jena, Germany, e-mail: nah@rz.uni-jena.de, wenzel@minet.uni-jena.de
Jörg Wenzel
Affiliation:
Mathematisches Institut, FSU Jena, D-07743 Jena, Germany, e-mail: nah@rz.uni-jena.de, wenzel@minet.uni-jena.de
Corresponding
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Abstract

A Banach space X has the average distance property if there exists a unique real number r such that for each positive integer n and all x1,…,xn in the unit sphere of X there is some x in the unit sphere of X such that

We show that lp does not have the average distance property if p > 2. This completes the study of the average distance property for lp spaces.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Hinrichs, A., ‘The average distance property of classical Banach spaces’, Bull. Austral. Math. Soc. 62 (2000), 119134.CrossRefGoogle Scholar
[2]Ledoux, M. and Talagrand, M., Probability in Banach spaces (Springer-Verlag, Berlin, Heidelberg, 1991).CrossRefGoogle Scholar
[3]Lin, P.-K., ‘The average distance property of Banach spaces’, Arch. Math. (Basel) 68 (1997), 496502.CrossRefGoogle Scholar
[4]Morris, S. A. and Nickolas, P., ‘On the average distance property of compact connected metric spaces’, Arch. Math. (Basel) 40 (1983), 459463.CrossRefGoogle Scholar

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