Timeline for An inequality in C*-algebras
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22, 2022 at 13:52 | comment | added | Ruy | An alternative argument, very much along @Jamie's comment, is that the operator norm is equal to the norm on the multiplier algebra $M(A)$ and, since $A$ is a proper ideal in $M(A)$, and hence contains no invertible elements, the distance from 1 to $A$ must be 1. | |
| Apr 22, 2022 at 11:23 | comment | added | Nik Weaver | @JamieGabe ah, I thought it would be a C*-algebra but I didn't remember why. I guess it's been a while since I read Pedersen ... | |
| Apr 22, 2022 at 7:58 | comment | added | Jamie Gabe | Alternatively, $\tilde A := $span$\{I\} \cup \pi(A)$ is a $C^*$-algebra (the unitisation of $A$), see for instance the proof of Prop. 1.1.3 in G. K. Pedersen's book on $C^*$-algebras. The map $\tilde A \to \mathbb C$ which annihilates $\pi(A)$ is a $\ast$-homomorphism, and such are always contractive (a fundamental consequence of the $C^*$-identity). | |
| Apr 22, 2022 at 1:35 | history | edited | Nik Weaver | CC BY-SA 4.0 |
deleted 5 characters in body
|
| Apr 22, 2022 at 0:43 | comment | added | LSpice | OK, I have made the edit. Thanks! | |
| Apr 22, 2022 at 0:42 | history | edited | LSpice | CC BY-SA 4.0 |
`\lVert\rVert` and `\lvert\rvert`
|
| Apr 22, 2022 at 0:21 | comment | added | Nik Weaver | @LSpice I see, thank you. Feel free to edit any of my answers for style! | |
| Apr 21, 2022 at 23:30 | history | answered | Nik Weaver | CC BY-SA 4.0 |