A geometry characteristic of Banach spaces with \(c^1\)-norm (Q2258091)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A geometry characteristic of Banach spaces with \(c^1\)-norm |
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A geometry characteristic of Banach spaces with \(c^1\)-norm (English)
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2 March 2015
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The main theorem of the paper under review establishes that the norm of a Banach space \(E\) is \(C^{1}\) in \(E \setminus \{0\}\) if and only if its unit sphere \(S\) is a \(C^{1}\)-submanifold of \(E\) with \(\operatorname{codim}S=1\).
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smooth norm
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