On non-midpoint locally uniformly rotund normability in Banach spaces - A. K. Mirmostafaee (International Journal of Mathematics and Mathematical Sciences)
We will show that if X is a tree-complete subspace of ℓ∞, which contains c0, then it does not admit any weakly midpoint locally uniformly convex renorming. It follows that such a space has no equivalent Kadec renorming.