We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach spaces. We derive basic properties of this Maslov index and emphasize the new features appearing.
Bibliografisk noteSubmitted, 24 July, 2012, Accepted (with suggestions for changes), 28 November 2012, Revised 30 January, 2013, Fully accepted 31 January, 2013
- Closed relations
- Fredholm pairs of Lagrangians
- Maslov index
- Spectral flow
- Symplectic splitting
- Weak symplectic structure