Aspects of the uniform λ-property


If Z is a uniformly convex normed space, the quotient space \ell_∈fty(Z)/c<sub>0</sub>(Z), which is not strictly convexifiable, is shown to have the unifonn λ -property and its  λ-function is calculated. An example is given of a Banach space X with a closed linear subspace Y such that Y and X/Y and strictly convex, yet X fails to have the λ- property. Convex sequences which generate B_{\ell_∈fty} are characterized.

DOI Code: 10.1285/i15900932v12p157

Keywords: Extreme point; Strict convexity; λ-property; Uniform convexity

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