0
$\begingroup$

I am reading a book "C*-algebras and Finite-Dimensional Approximations". There is a quotation below:

For infinite-dimensional Hilbert space $H$ and a abelian von Neumann algebra $A$, we can represent $A\bar{\otimes}\mathbb{B}(H)\subset \mathbb{B}(K\otimes H),$ where $A\subset \mathbb{B}(K)$ is any faithful normal representation.

I can not comprehend why we can represent $A\bar{\otimes}\mathbb{B}(H)\subset \mathbb{B}(K\otimes H)$. Maybe I am lack of some knowledge points. Could someone explain to me ?

$\endgroup$
2
$\begingroup$

By definition, $A\bar\otimes B(H)$ is the von Neumann algebra generated by $A\otimes1$ and $1\otimes B(H)$ in $B(K\otimes H)$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.