Iteration formulae of the Maslov-type index theory in weak symplectic   Hilbert spaces
  In this paper, we prove a splitting formula for the Maslov-type indices of symplectic paths induced by the splitting of the nullity in weak symplectic Hilbert space. Then we give a direct proof of iteration formulae for the Maslov-type indices of symplectic paths. 
Li Wu and Chaofeng Zhu
math.DS math.SG