The classification of bf Z-graded modules of the intermediate series over the q-analog Virasoro-like algebra

In this paper, we complete the classification of the {\bf Z}-graded modules of the intermediate series over the $q$-analog Virasoro-like algebra $L$. We first construct four classes of irreducible {\bf Z}-graded $L$-modules of the intermediate series. Then we prove that any {\bf Z}-graded $L$-modules of the intermediate series must be the direct sum of some trivial $L$-modules or one of the modules constructed by us.