# Direct product of operators

1. Aug 7, 2013

### LagrangeEuler

Is this correct in infinite dimensional Hilbert spaces?
$(\hat{A}_1 \otimes \hat{A}_2)^{-1}=\hat{A}^{-1}_1 \otimes \hat{A}^{-1}_2$
$(\hat{A}_1 \otimes \hat{A}_2)^{\dagger}=\hat{A}^{\dagger}_1 \otimes \hat{A}^{\dagger}_2$
$(\hat{A}_1 +\hat{A}_2) \otimes \hat{A}_3=(\hat{A}_1 \otimes \hat{A}_2)+(\hat{A}_2 \otimes \hat{A}_3)$
$\hat{A}_1 \otimes (\hat{A}_2+\hat{A}_3)=(\hat{A}_1 \otimes \hat{A}_2)+(\hat{A}_1 \otimes \hat{A}_3)$
$\hat{1} \otimes \hat{1}=\hat{1}$
$(\hat{A}_1 \otimes 0)=(0 \otimes \hat{A}_2)=0$
Can you tell me a book where I can see this properties. I found this only for operators which acts in finite dimensional Hilbert spaces.

2. Aug 14, 2013