In this paper, the Rotenberg model with general boundary conditions in bacterial population growth is discussed by using linear operator theory in $L_p(1<p<\mathrm{\infty })$ space. Compact operator $(\lambda I-B_H{)}^{-1}K$ and boundedness of operator $|\mathrm{I}\mathrm{m}\lambda \mid \parallel [(\lambda I-B_H{)}^{-1}K(\lambda I-B_H{)}^{-1}{]}^{m}K(\lambda I-A_H{)}^{-1}\parallel (|\mathrm{I}\mathrm{m}\lambda |\to +\mathrm{\infty })$ in a certain band domain are proved by using comparison operator and resolving operator. The results of spectral existence of the corresponding migration operator and asymptotic stability of the solution of the corresponding transport equation are obtained.