  Quantum Lefschetz theorem by Coates and Givental gives a relationship between
the genus 0 Gromov-Witten theory of X and the twisted theory by a line bundle L
on X. We prove the convergence of the twisted theory under the assumption that
the genus 0 theory for original X converges. As a byproduct, we prove the
semi-simplicity and the Virasoro conjecture for the Gromov-Witten theories of
(not necessarily Fano) projective toric manifolds.
