- #1
LagrangeEuler
- 717
- 20
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.
## (\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.