I'm reading the book about neural networks from Simon Haykin.
In the first section of recurrent neural networks plot this figure:
and he says that the system is linear. So he discribes the system in the following manner: $$y_k(n) = A[x'_j] (I)$$
And $$x'_j = x_j(n) + B[y_k(n)] (II)$$
He tells that $A$ and $B$ are "operators", and then he gets the closed-loop operator: $$y_k(n) = \dfrac{A}{1-AB}[x_j(n)]$$ which is a operator too.
My question is, it looks like he just substituted $x'_j$ from $(II)$ into $(I)$ to get this result. But, since they are operators, a number-like algebra shouldn't be allowed. Am i missing some concept of operator?