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
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 25, 2019 at 19:42 | comment | added | Student | Thank you very much but please why in the expressions of $A_1$ and $A_2$, you start with $y_2$ and not $y_1$? | |
| Apr 25, 2019 at 13:59 | comment | added | hänsel | $A_1(x_1,x_2,x_3,⋯⊕y_2,y_3,…)=(0,x_1,x_2,x_3,...⊕0,0,0,....)$. | |
| Mar 25, 2019 at 11:15 | comment | added | Student | Please what is explicitely the expresion of $A_1$? Thanks | |
| Jan 28, 2019 at 12:02 | comment | added | hänsel | $A_1$ yes. but you have double-size Hilbert space $\ell^2(\mathbb{N}) \oplus \ell^2(\mathbb{N}) $. $A_2(x_1,x_2,x_3, \dots \oplus y_2,y_3,\ldots)=(0,\ldots \oplus x_1,y_2,y_3,y_4,\ldots)$. | |
| Jan 27, 2019 at 18:57 | comment | added | Student | Thanks for the second answer. $A_1: \ell_{\mathbb{N}^*}^2(\mathbb{C})\rightarrow \ell_{\mathbb{N}^*}^2(\mathbb{C})$ be defined by $$A_1(x_1,x_2,\cdots)=(0,x_1,x_2,\cdots),$$ Please what is the difference between $A_1$ and $A_2$? | |
| Jan 27, 2019 at 15:55 | history | answered | hänsel | CC BY-SA 4.0 |