Let $A$ be a c*-algebra, then the positive elements in $M_{n}(A)$ are ultraweakly dense in the positive part of $M_{n}(A^{**})$. I do not know how to prove this conclusion. Could someone show me more details.
2026-03-27 01:24:27.1774574667
A question about ultraweakly dense
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Since you already know that $M_n(A^{**})=M_n(A)^{**}$, the matrices are playing no role here. So all you need to show is that $A_+$ is ultraweakly dense in $A^{**}_+$.