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Nonexpansive projections onto two-dimensional subspaces of Banach spaces

Published online by Cambridge University Press:  17 April 2009

Bruce Calvert  and
Simon Fitzpatrick
Bruce Calvert
Affiliation:
Department of Mathematics and Statistics, The University of AucklandPrivate Bag, Auckland, New Zealand
Simon Fitzpatrick
Affiliation:
Department of Mathematics and Statistics, The University of AucklandPrivate Bag, Auckland, New Zealand
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Abstract

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We show that if a three dimensional normed space X has two linearly independent smooth points e and f such that every two-dimensional subspace containing e or f is the range of a nonexpansive projection then X is isometrically isomorphic to ℓp(3) for some p, 1 < p ≤ ∞. This leads to a characterisation of the Banach spaces c0 and ℓp, 1 < p ≤ ∞, and a characterisation of real Hilbert spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 1 , February 1988 , pp. 149 - 160
Copyright
Copyright © Australian Mathematical Society 1988

References

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