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, we prove that there exists a dual norm such that its unit sphere is weak metrizable if and only if BX,w is a descriptive compact, which provides a complete characterization.
Weakly Metrizability of Spheres and Renormings of Banach Spaces
Ferrari S.;
2016-01-01
Abstract
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, we prove that there exists a dual norm such that its unit sphere is weak metrizable if and only if BX,w is a descriptive compact, which provides a complete characterization.File in questo prodotto:
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