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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It was answered here a long time ago. You search along the site. – Norbert Jan 19 '15 at 00:10
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@userNaN : I could not find it. If it's possible, please answer it again. – niki Jan 20 '15 at 04:37
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1you should ask Martin Argerami. His a main specialist on operator algebras here. – Norbert Jan 20 '15 at 09:12
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@MartinArgerami : If possible, please give me a hint about this question. – niki Jan 20 '15 at 12:46
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@niki: AFAIK, you cannot ping people that have not contributed to the thread. – C-star-W-star Jul 22 '15 at 15:54
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@niki: Here you can find a proof: Trace Class – C-star-W-star Jul 25 '15 at 11:49