ASPLUND SPACES AND DECOMPOSABLE NONSEPARABLE BANACH-SPACES

We show that an Asplund space of density character N-1 is weakly compactly generated if and only if it has a projectional resolution of identity for each equivalent norm. We show that every nonseparable Asplund space has a nonseparable subspace which has an equivalent strictly convex norm. We give an example of a non-Asplund space such that every bounded weakly closed subset is an intersection of finite union of balls. We show the existence of an Eberlein compact K such that (C(K),parallel to.parallel to infinity) has no lambda-norming Markushevich basis if lambda < 2.