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We know that two unital matrix algebras are isomorphic only if completely isometric. But when is a unital subspace of $N \times N$ matrices completely isometric to a matrix algebra? Can we describe this using matrix norms?

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What (if anything) does Paulsen's book say? –  Yemon Choi Jul 26 '10 at 18:06
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It may also be worth giving a brief account of your motivation for this question, which sources you're familiar with, or what level you are at. This would make it easier for people to focus their answers to your question. –  Yemon Choi Jul 26 '10 at 18:09

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