In this work, we study the localized $CP$ violation in $B^-\rightarrow K^-��^+��^-$ and $B^-\rightarrow K^- ��(600)$ decays by employing the quasi two-body QCD factorization approach. Both the resonance and the nonresonance contributions are studied for the $B^-\rightarrow K^-��^+��^-$ decay. The resonance contributions include those not only from $[����]$ channels including $��(600)$, $��^0(770)$ and $��(782)$ but also from $[K��]$ channels including $K^*(892)$, $K_0^*(1430)$, $K^*(1410)$, $K^*(1680)$ and $K_2^*(1430)$. By fitting the experimental data $\mathcal{A_{CP}}(K^-��^+��^-)=0.678\pm0.078\pm0.0323\pm0.007$ for $m_{K^-��^+}^2<15$ $\mathrm{GeV}^2$ and $0.08

arXiv admin note: text overlap with arXiv:0704.1049 by other authors