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!
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?