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I am trying to grok matrix ordered operator algebras, but I am having a hard time understanding their significance from the definition. Here is the definition (or at least, one way of stating it): ...

The aim of this question is to collect nice maps on $M_n(\mathbb{C})$ with the following property: $\phi_n:M_n(\mathbb{C})\rightarrow M_n(\mathbb{C})$ with $||\phi||=1$ and $||\phi_n||_{cb}\...