Article contents
Lushness, Numerical Index 1 and the Daugavet Property in Rearrangement Invariant Spaces
Published online by Cambridge University Press: 20 November 2018
Abstract
We show that for spaces with 1–unconditional bases lushness, the alternative Daugavet property and numerical index 1 are equivalent. In the class of rearrangement invariant (r.i.) sequence spaces the only examples of spaces with these properties are ${{c}_{0,}}{{\ell }_{1}}$ and ${{\ell }_{\infty }}$. The only lush r.i. separable function space on $\left[ 0,1 \right]$ is ${{L}_{1}}\left[ 0,1 \right]$; the same space is the only r.i. separable function space on $\left[ 0,1 \right]$ with the Daugavet property over the reals.
Keywords
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 2013
References
- 8
- Cited by