[Banach] Abstract of a paper by Antonio Aviles

This is an announcement for the paper "Radon-Nikodym compact spaces of low weight and Banach spaces" by Antonio Aviles.

Abstract: We prove that a continuous image of a Radon-Nikod'{y}m compact space of weight less than b is Radon-Nikod'{y}m compact. As a Banach space counterpart, subspaces of Asplund generated Banach spaces of density character less than b are Asplund generated. In this case, in addition, there exists a subspace of an Asplund generated space which is not Asplund generated which has density character exactly b.

Archive classification: math.FA math.GN

Mathematics Subject Classification: Primary 46B26, Secondary 46B22, 46B50, 54G99

Citation: Studia Math. 166 (2005), no. 1, 71–82

Submitted from: avileslo@um.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1012.5512

or

http://arXiv.org/abs/1012.5512