CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Publicationsjournals
Publications        
Search results

Search: All articles in the CJM digital archive with keyword numerical index

  Expand all        Collapse all Results 1 - 1 of 1

1. CJM 2012 (vol 65 pp. 331)

Kadets, Vladimir; Martín, Miguel; Merí, Javier; Werner, Dirk
Lushness, Numerical Index 1 and the Daugavet Property in Rearrangement Invariant Spaces
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 $[0,1]$ is $L_1[0,1]$; the same space is the only r.i. separable function space on $[0,1]$ with the Daugavet property over the reals.

Keywords:lush space, numerical index, Daugavet property, Köthe space, rearrangement invariant space
Categories:46B04, 46E30

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/