A symbol of commuting ranges in tensor product

Question

Here is a proposition of tensor product: ($A,~B,~C$ are C*-algebras)

Proposition 3.1.17 Given two *-homomorphisms $\pi_{A}: A\rightarrow C$ and $\pi: B\rightarrow C$ with commuting ranges (i.e., $[\pi_{A}(a), \pi_{B}(b)]=0$ for all $a\in A$, $b\in B$), the product map $\pi_{A} \times \pi_{B}: A\odot B\rightarrow C$ is also a *-homomorphism.

However, I do not know what does the commuting ranges mean. I mean what is $[\pi_{A}(a), \pi_{B}(b)]$?

Answer 1

$[x,y]=xy-yx$ is the commutator of $x$ and $y$.