Timeline for Need a reference of a fact given in B. Blackadar's Operator Algebras
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 20, 2019 at 10:27 | vote | accept | Math Lover | ||
| Feb 11, 2019 at 10:35 | comment | added | Mateusz Wasilewski | I haven't checked the details, but I suppose so. One point which might be important, is that a non-unital algebra is an ideal in its unitisation and inclusions of ideals interact nicely with the maximal tensor product (which is not the case for arbitrary inclusions). | |
| Feb 11, 2019 at 10:09 | comment | added | Math Lover | Thank you. For non unital case do we need to proceed by adjoining identity or some other way? | |
| Feb 11, 2019 at 8:43 | comment | added | Mateusz Wasilewski | It really follows from the definition: the norm in the maximal tensor product is computed as the supremum of the norms under pairs of $\ast$-homomorphisms with commuting ranges. On the other hand, if we are given a $\ast$-homomorphism from the tensor product $A\otimes B$ (of unital algebras), we get a pair of homomorphisms with commuting ranges by restricting to $A\otimes \mathrm{1}$ and $1\otimes \mathrm{B}$. | |
| Feb 9, 2019 at 7:03 | comment | added | Math Lover | Sorry can you give a reference for universal property of maximal tensor product? Thank you very much! | |
| Feb 8, 2019 at 10:32 | history | answered | Mateusz Wasilewski | CC BY-SA 4.0 |