A representation of von Neumann algebra of type I

Question

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 ?

Answer 1

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