Timeline for Hölder's inequality for Hilbert-Schmidt operators which are also trace class
Current License: CC BY-SA 4.0
6 events
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| Feb 19, 2023 at 2:57 | history | edited | Jukka Kohonen | CC BY-SA 4.0 |
correct Hölder's in title etc.
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| Apr 13, 2018 at 19:55 | comment | added | Nik Weaver | Probably in Dunford-Schwartz, likely in Conway. The $p=1$, $q = \infty$ inequality is in chapter 6 of my book Mathematical Quantization. | |
| Apr 13, 2018 at 15:21 | comment | added | Another Grad student | Thanks! Yes I mean $|<A,B>|$. Can you point me to a reference (textbook, paper)? | |
| Apr 13, 2018 at 5:54 | comment | added | Nik Weaver | (I assume you mean $|\langle A, B\rangle|$, not $\langle A,B\rangle$.) | |
| Apr 13, 2018 at 5:53 | comment | added | Nik Weaver | Yes, this is standard stuff. Note that any trace class operator belongs to all the Schatten $p$-spaces. We do have a Holder inequality. In fact, if $A$ is trace class and $B$ is any bounded operator then $|tr(AB^*)| \leq \|A\|_1 \|B\|$. You should be able to find this in most textbooks. | |
| Apr 12, 2018 at 18:52 | history | asked | Another Grad student | CC BY-SA 3.0 |