Generalization of Zippin’s theorem on perturbing Banach spaces with separable dual
Volume 245 / 2019
Studia Mathematica 245 (2019), 169-183 MSC: Primary 46B20; Secondary 46B26. DOI: 10.4064/sm170619-30-11 Published online: 20 July 2018
We generalize a result on Banach spaces with separable dual which was first shown by Zippin, and was explicitly formulated by Benyamini. We prove that there is a class of Asplund spaces, which includes all spaces with separable dual, whose members can be perturbed inside a suitable ambient space to be contained in the space of continuous functions on a well-founded compact tree.