Article contents
Nonexpansive projections onto two-dimensional subspaces of Banach spaces
Published online by Cambridge University Press: 17 April 2009
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.
- 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
- 1
- Cited by