The Maslov index in weak symplectic functional analysis
Institution: | Roskilde University |
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Department: | |
Year: | 2013 |
Keywords: | Closed relations; Fredholm pairs of Lagrangians; Maslov index; Spectral flow; Symplectic splitting; Weak symplectic structure; Closed relations; Fredholm pairs of Lagrangians; Maslov index; Spectral flow; Symplectic splitting; Weak symplectic structure |
Record ID: | 1120139 |
Full text PDF: | http://arxiv.org/abs/1301.7248 |
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.; 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.