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Metrization theory and the Kadec property. (English) Zbl 1351.46002
Summary: The uniform structure of a descriptive normed space \((X,\| \cdot\|)\) always admits a description with an \((F)\)-norm \(\| \cdot\|_{1}\) such that weak and norm topologies coincide on \[ \{x\in X:\| x\|_{1}=\rho\} \] for every \(\rho> 0\).

MSC:
46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
46B03 Isomorphic theory (including renorming) of Banach spaces
46B20 Geometry and structure of normed linear spaces
46B26 Nonseparable Banach spaces
54E35 Metric spaces, metrizability
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References:
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