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The average distance property of classical Banach spaces II

Published online by Cambridge University Press:  17 April 2009

Aicke Hinrichs  and
Jörg Wenzel
Aicke Hinrichs
Affiliation:
Mathematisches Institut, FSU Jena, D-07743 Jena, Germany, e-mail: [email protected], [email protected]
Jörg Wenzel
Affiliation:
Mathematisches Institut, FSU Jena, D-07743 Jena, Germany, e-mail: [email protected], [email protected]
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Abstract

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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
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 3 , June 2002 , pp. 511 - 520
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Hinrichs, A., ‘The average distance property of classical Banach spaces’, Bull. Austral. Math. Soc. 62 (2000), 119–134.CrossRefGoogle Scholar
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