The Maslov index in weak symplectic functional analysis

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Abstract

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.
Original languageEnglish
JournalAnnals of Global Analysis and Geometry
Volume44
Issue number3
Pages (from-to)283-318
Number of pages36
ISSN0232-704X
DOIs
Publication statusPublished - Oct 2013

Keywords

  • Closed relations
  • Fredholm pairs of Lagrangians
  • Maslov index
  • Spectral flow
  • Symplectic splitting
  • Weak symplectic structure

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