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Timeline for Regarding unital positive operators

Current License: CC BY-SA 4.0

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Jul 19, 2021 at 19:05 comment added Jochen Glueck @Ma18: Sure, feel free to write me.
Jul 19, 2021 at 17:13 comment added Ma18 @JochenGlueck Can I approach you for research collaboration/ discussion via mail?
May 24, 2021 at 14:23 comment added Jochen Glueck @user31459: Hmm, I'm not sure I understand your question then. Could you clarifiy what you mean by "suffice if $T$ is bounded?" Which assumption in my post would you like to relax to boundedness? (Note that Nik Weaver's answer below already shows that this does not hold for gerenal bounded operators which are positive and unital.)
May 24, 2021 at 14:20 comment added user31459 No the condition $T1=1$ included.
May 24, 2021 at 14:16 comment added Jochen Glueck @user31459: Do you mean without a condition of the kind $T1 = 1$? This won't in general: just let $T$ be the multiplication with a non-negative continuous function $m$ that is $0$ at a certain point.
May 24, 2021 at 13:58 comment added user31459 So will it suffice if T is bounded?
Oct 24, 2020 at 16:48 history edited Jochen Glueck CC BY-SA 4.0
Corrected a few typos.
Oct 24, 2020 at 2:41 history answered Jochen Glueck CC BY-SA 4.0