Timeline for Description of state space of $C(K,M_n)$?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 27, 2022 at 8:04 | comment | added | C-star-W-star | Hi Tobias, indeed we’re working on such a problem. Also thanks for the suggestion about your paper! :) | |
| May 26, 2022 at 13:54 | comment | added | Tobias Fritz | By the way, are you working on a moment problem on $C^*(\mathbb{Z}/2 \times \mathbb{Z}/2)$? I solved one such problem myself in this paper, so perhaps it's related. (It's been my first paper ever, and the writing is a bit quirky... See in particular App A in there.) | |
| May 26, 2022 at 13:54 | comment | added | Tobias Fritz | The states on $C(K,M_n)$ are exactly the Radon measures on $K$ that take values in positive linear functionals on $M_n$, and are normalized such that the measure of $K$ itself is a state on $M_n$. One way to see this is to simply look at a state entry-wise on the matrix, which is then a bounded linear functional on $C(K)$. | |
| May 26, 2022 at 13:42 | history | edited | C-star-W-star | CC BY-SA 4.0 |
Added: closed convex hull
|
| May 26, 2022 at 13:35 | comment | added | C-star-W-star | Good point, thanks! So I added on their closed convex hull. | |
| May 26, 2022 at 13:34 | history | edited | C-star-W-star | CC BY-SA 4.0 |
Added: closed convex hull
|
| May 26, 2022 at 10:23 | history | asked | C-star-W-star | CC BY-SA 4.0 |