I have read a definition of isomorphism as bijective isometry. I was also showed a definition that isomorphism is a bijective map where both the map and its inverse are bounded (perhaps only for normed spaces??). This does not seem to be the same thing as an isometry.(adsbygoogle = window.adsbygoogle || []).push({});

For example, the poisson problem, from H^1_0 to H^-1 (dual space of H^1_0), is bijective by Lax Milgram, and I can show both maps (the original and the inverse) are bounded. But showing an isometry doesn't seem possible.

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# Isometry and isomorphism

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