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Full Description
The authors consider a curve of Fredholm pair of Lagrangian subspaces in a fixed Banach space with continuously varying weak symplectic structures. Assuming vanishing index, they obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using such decompositions the authors define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. The authors prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction while recovering all the standard properties of the Maslov index.
As an application, the authors consider curves of elliptic operators which have varying principal symbol, varying maximal domain and are not necessarily of Dirac type. For this class of operator curves, the authors derive a desuspension spectral flow formula for varying well-posed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral flow on partitioned manifolds.
Contents
Introduction
Part 1. Maslov index in symplectic Banach spaces: General theory of symplectic analysis in Banach spaces
The Maslov index in strong symplectic Hilbert space
The Maslov index in Banach bundles over a closed interval
Part 2. Applications in global analysis: The desuspension spectral flow formula
Appendix A. Perturbation of closed subspaces in Banach spaces
Bibliography
List of symbols
Index of names/authors
Subject index
Index
Bibliography
