Timeline for A question on $Z^{*}$ algebras
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 29, 2014 at 10:37 | comment | added | Narutaka OZAWA | The most typical example is the transpose map $T$ on $B(\ell_2)$, which is positive but not completely positive and $T\otimes\mathrm{id}_{B(\ell_2)}$ is unbounded. See e.g., mathoverflow.net/questions/86550/… | |
| Jun 29, 2014 at 10:24 | comment | added | Ali Taghavi | according to your last comment, what is an example of two bounded linear maps $\phi_{i}:A_{i}\to B_{i}\;\;,i=1,2$ such that $\phi_{1}\otimes \phi_{2}$ is not a bounded operator on minimal tensor product $A_{1} \otimes_{min} A_{2}$? | |
| Jun 27, 2014 at 23:49 | vote | accept | Ali Taghavi | ||
| Jun 27, 2014 at 23:18 | comment | added | Narutaka OZAWA | One needs complete positivity for well-definedness of $\phi_1\otimes\phi_2$. | |
| Jun 27, 2014 at 22:42 | comment | added | Ali Taghavi | thank you very much for your very interesting answer. In the proof of the lemma where did you used "completely" that is $M_{n}(A)$? | |
| Jun 27, 2014 at 22:27 | history | answered | Narutaka OZAWA | CC BY-SA 3.0 |