Journal Article

WEAKLY METRIZABILITY OF SPHERES AND RENORMINGS OF BANACH SPACES

S. Ferrari, J. Orihuela and M. Raja

in The Quarterly Journal of Mathematics

Volume 67, issue 1, pages 15-27
Published in print March 2016 | ISSN: 0033-5606
Published online January 2016 | e-ISSN: 1464-3847 | DOI: https://dx.doi.org/10.1093/qmath/hav038

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We study the metrizability of weak topologies when restricted to the unit sphere of some equivalent norm on a Banach space, and its relationships with other geometrical properties of norms. In case of dual Banach space [math] we prove that there exists a dual norm such that its unit sphere is weak[math] metrizable if and only if [math] is a descriptive compact, which provides a complete characterization.

Journal Article.  5777 words. 

Subjects: Pure Mathematics