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Let $A\in B(H)$ and $\sum_{E}|\langle A e,e\rangle|< \infty$ for every orthonormal basis $E$. Show that $A$ is a trace class (means $\sum_E \langle |A|e,e\rangle < \infty$). I can not prove it. Please give me a hint. Thanks.

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  • $\begingroup$ It was answered here a long time ago. You search along the site. $\endgroup$ – Norbert Jan 19 '15 at 0:10
  • $\begingroup$ @userNaN : I could not find it. If it's possible, please answer it again. $\endgroup$ – niki Jan 20 '15 at 4:37
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    $\begingroup$ you should ask Martin Argerami. His a main specialist on operator algebras here. $\endgroup$ – Norbert Jan 20 '15 at 9:12
  • $\begingroup$ @MartinArgerami : If possible, please give me a hint about this question. $\endgroup$ – niki Jan 20 '15 at 12:46
  • $\begingroup$ @niki: AFAIK, you cannot ping people that have not contributed to the thread. $\endgroup$ – C-Star-W-Star Jul 22 '15 at 15:54

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