Aspects of the uniform λ-property

Abstract

If Z is a uniformly convex normed space, the quotient space $\ell_∈fty(Z)/c₀(Z)$, 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.