Aspects of the uniform λ-property
Abstract
If Z is a uniformly convex normed space, the quotient space
, which is not strictly convexifiable, is shown to have the unifonn λ -property and its
-function is calculated. An example is given of a Banach space X with a closed linear subspace Y such that Y and
and strictly convex, yet X fails to have the λ- property. Convex sequences which generate
are characterized.
![\ell_∈fty(Z)/c<sub>0</sub>(Z)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/0891b036c958135a555c4b3121d42b8b.png)
![λ](http://siba-ese.unile.it/plugins/generic/latexRender/cache/d56b053d93b2b95ded25f9916fe1a22d.png)
![X/Y](http://siba-ese.unile.it/plugins/generic/latexRender/cache/cf5449f4d6140dde6f3fe7715ab183da.png)
![B_{\ell_∈fty}](http://siba-ese.unile.it/plugins/generic/latexRender/cache/e096ff6bcb63032866155ff4c59cf621.png)
DOI Code:
10.1285/i15900932v12p157
Keywords:
Extreme point; Strict convexity; λ-property; Uniform convexity
Full Text: PDF