Convergence of Infinite Series in Bosonic Second Quantization
  The functor of second quantization as well as quadratic creation and annihilation operators on the bosonic Fock space are defined through possibly infinite series. The domain of convergence is investigated by precise number operator estimates and the Banach-Steinhaus Theorem. Some fundamental properties of the limit operators are derived. 
Peter Otte
math-ph math.FA math.MP