Diameter 2 properties and convexity
Volume 232 / 2016
Studia Mathematica 232 (2016), 227-242
MSC: Primary 46B04, 46B20.
DOI: 10.4064/sm8317-4-2016
Published online: 25 April 2016
Abstract
We present an equivalent midpoint locally uniformly rotund (MLUR) renorming of $C[0,1]$ with the diameter 2 property (D2P), i.e. every non-empty relatively weakly open subset of the unit ball has diameter 2. An example of an MLUR space with the D2P and with convex combinations of slices of arbitrarily small diameter is also given.
