Nonexpansive projections onto two-dimensional subspaces of Banach spaces
- 1 February 1988
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 37 (1) , 149-160
- https://doi.org/10.1017/s000497270000424x
Abstract
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.Keywords
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