Publication Date:
2016-03-08
Description:
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 $X^{\ast },$ we prove that there exists a dual norm such that its unit sphere is weak $^{\ast }$ metrizable if and only if $(\mathscr {B}_{X^{\ast }},w^{\ast })$ is a descriptive compact, which provides a complete characterization.
Print ISSN:
0033-5606
Electronic ISSN:
1464-3847
Topics:
Mathematics
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