Timeline for "Identity tensor transpose" as a map $M_n \hat{\otimes} M_n \to M_n \overline{\otimes} M_n$
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 4, 2016 at 14:08 | vote | accept | Yemon Choi | ||
| May 9, 2016 at 20:04 | comment | added | Yemon Choi | @MatthewDaws Thanks - I thought I remembered seeing it when trying to prove something else. I can prove the BSp version by hand (checked this after your comment) which made be 95% sure the OS version should work... | |
| May 9, 2016 at 19:54 | comment | added | Matthew Daws | This is Proposition 8.1.10 in Effros-Ruan. | |
| May 7, 2016 at 16:36 | comment | added | Yemon Choi | Alternatively, I think I remember reading in Effros-Ruan that there is a tensor interchange map for $\hat{\otimes}$ and $\otimes_{\min}$, which should go $E \hat{\otimes} (F \otimes_{\min} G) \to (E\hat{\otimes} F) \otimes_{\rm min} G$. Repeated use of this seems to then yield a complete contraction from the first thing in your comment to the second one. | |
| May 7, 2016 at 15:53 | comment | added | Yemon Choi | Good point - this is the part I was sweeping under the carpet. I guess I could try to duck the issue by saying that the LHS certainly embeds completely contractively into "B(V) Haagerup midlle thing Haagerup B(W)", then the" middle" is compact operators W to V, and we know that multiplication of op algebras is bounded wrt Haagerup tensor product. (This was my original line of thought) | |
| May 7, 2016 at 12:46 | comment | added | Matthew Daws | It seems to me you implicitly re-bracket $B(V) \ptp( V\itp W^*) \ptp B(W)$ to $(B(V) \ptp V)\itp (W^* \ptp B(W))$ in order to then apply your two maps. Why can you do that? | |
| May 5, 2016 at 17:51 | history | edited | Yemon Choi | CC BY-SA 3.0 |
fixed a typo and made some other minor improvements
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| May 4, 2016 at 19:27 | history | answered | Yemon Choi | CC BY-SA 3.0 |