  Estimates for eigenvalues of Schr\"{o}dinger operators on the half-line with
complex-valued potentials are established. Schr\"{o}dinger operators with
potentials belonging to weak Lebesque's classes are also considered. The
results cover those known previously due to R. L. Frank, A. Laptev and R.
Seiringer [In spectral theory and analysis, vol. 214, Oper. Theory Adv. Appl.,
pag. 39-44; Birkh\"{a}user/Springer Basel.]
