Timeline for $\sum_{k=1}^dA_k^*A_k$ and $\sum_{k=1}^dA_kA_k^*$ have the same norms if $A_k$ are commuting
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 27, 2019 at 15:20 | vote | accept | Student | ||
| Jan 27, 2019 at 15:02 | comment | added | hänsel | partial isometry is $A$ with $A A^* A=A$, and copies isometrically the source Hilbert space $A^* A (H)$ to $AA^*(H)$, see lietrature. you may take $H_1=H_2=H_2 =\mathbb{C}$, and $A_1,A_2$ 3x3 matrices, where $A_1(e_1)=e_2$, otherwise 0, and $A_2(e_1)=e_3$, otherwise 0, where $e_1,e_2,e_3$ canoncal basis of $\mathbb{C}^3$. | |
| Jan 27, 2019 at 14:55 | comment | added | hänsel | on the Hilbert space $H_1 \oplus H_2 \oplus H_3$ | |
| Jan 27, 2019 at 14:54 | comment | added | Student | the operators $A_k$ are acting on the same Hilbert space $E$ | |
| Jan 27, 2019 at 14:49 | history | answered | hänsel | CC BY-SA 4.0 |