Timeline for Range of a trace preserving completely positive projection
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 16, 2015 at 16:41 | comment | added | P Vanchinathan | Request Eckhardt to make the comment into an answer and H\'ector to accept it so that the question does not end up as showing unanswered. | |
| Mar 16, 2015 at 16:16 | comment | added | Caleb Eckhardt | Take a positive operator $B$ that is not a multiple of a projection with $\textrm{Tr}(B)=1$ and define $P(A)=\textrm{Tr}(A)B.$ Then the range is 1 dimensional but $B$ doesn't generate a 1 dimensional C*-algebra. | |
| Mar 16, 2015 at 16:08 | comment | added | Héctor | @ChrisHeunen I've already saw that, i'm aware you can abstractly view $\text{Ran}(P)$ as a W* algebra with Choi-Effros product. But i don't think that is relevant for my question, i look results with the same product that inherits from $M_n(\mathbb{C})$. I know that if you change the trace preserving condition by unital, the conclusion i look for is false. But i can't produce counterexamples for the case trace preserving (unital AND trace preserving guarantee the conclusion). | |
| Mar 16, 2015 at 16:00 | comment | added | Chris Heunen | See also mathoverflow.net/q/42022/10368 | |
| Mar 16, 2015 at 9:40 | history | edited | Héctor | CC BY-SA 3.0 |
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| Mar 16, 2015 at 9:35 | review | First posts | |||
| Mar 16, 2015 at 9:39 | |||||
| Mar 16, 2015 at 9:31 | history | asked | Héctor | CC BY-SA 3.0 |