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Post Closed as "not a real question" by Bill Johnson, Qiaochu Yuan, Deane Yang, Chris Godsil, algori
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Let $\mathcal{X}$ be a vector space, $| \cdot |$ and $\| \cdot \|$ be two norms on which $\mathcal{X}$ is complete with respect to both. Can the two norms be not equivalent? Please just give me some hint, I want to be able to do it myself. Thx! |
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Comparable Norm on BanachLet $\mathcal{X}$ be a vector space, $| \cdot |$ and $\| \cdot \|$ be two norms on which $\mathcal{X}$ is complete with respect to both. Can the two norms be not equivalent?
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