Timeline for Does the following tracial inequality (involving certain function applications) hold for positive semi-definite matrices?
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5 events
| when toggle format | what | by | license | comment | |
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| Jul 12, 2021 at 0:32 | comment | added | Narutaka OZAWA | Yes, that's my understanding. | |
| Jul 9, 2021 at 16:45 | comment | added | Lise Wouters | Thanks. I realize now that I actually wanted the inequality to hold in this more general sense, but it seems from the reference to Connes' paper that it is impossible. I'm not too familiar with the $L^1(N,\tau)$ appearing in Remark 1.2.7 so I wanted to verify if I understood correctly why this remark shows it's impossible. Is the reasoning behind this that if a constant $K$ would exist such that the inequality holds for all finite rank operators in $\mathcal{B}(\mathcal{H})$, then the inequality would also hold for all of $L^1(\mathcal{B}(\mathcal{H}))$, contradicting remark 1.2.7? | |
| Jul 9, 2021 at 6:13 | comment | added | Narutaka OZAWA | Well, it seems Connes says it's not possible if $U^*AU$ is replaced with another positive semidefinite $B$. See Remark 1.2.7 in his Annals paper 1976. doi.org/10.2307/1971057 | |
| Jul 8, 2021 at 14:10 | review | First posts | |||
| Jul 8, 2021 at 14:32 | |||||
| Jul 8, 2021 at 14:08 | history | asked | Lise Wouters | CC BY-SA 4.0 |