Timeline for Relation between tracial norm and operator norm on a von Neumann algebra
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 7, 2018 at 13:06 | comment | added | Adrián González Pérez | I meant that $S^\perp \cap \mathcal{A}$ should be dense inside $S^\perp$ not in $\mathcal{A}$. In any case the argument just need that $S^\perp \cap \mathcal{A}$ is not empty for every finite dimensional $S$. If that is the case, we can choose $x \in S^\perp \cap \mathcal{A}$ to be of $\| \cdot \|_{\mathcal{A}}$-norm one at every step. That will give an orthogonal base $(b_i)_i$ with $\| b_i \|_{\mathcal{A}} = 1$ but it may not be true that $\| b_i \|_{\phi} = 1$. | |
| Feb 6, 2018 at 21:42 | comment | added | Jesse Peterson | I don't understand how $S^\perp \cap \mathcal A$ can ever be dense in $\mathcal A$ if we have a non-trivial set $S \subset \mathcal A$. What topology are you using? | |
| Jan 26, 2018 at 17:08 | history | edited | Adrián González Pérez | CC BY-SA 3.0 |
added 22 characters in body
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| Jan 26, 2018 at 16:48 | history | answered | Adrián González Pérez | CC BY-SA 3.0 |