signal processing – Is this notation$~X(z)=Zleft[xleft[nright]right](z)$ of Z-transform correct?

The textbook which I have wrote the below equation of Z-transform.

$$X(z)=Z(x(n))$$

From the definition of Z-transform, the rightmost term of sigma is held.

$$X(z)=Z(x(n))=sum_{n=-infty}^{+infty} x(n )cdot z^{-n}$$

Of course the result of the computations of sigma only has $z$ as a variable so I thought the middle term can be rewritten as below.

$$X(z)=Z(x(n))(z)~~leftarrow~~text{Added (z) to emphasize that the function has variable z}$$

Is this notation not general or weird or can be subtracted of score of test?