The Maslov Index in Symplectic Banach Spaces

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Cover Title page Contents List of Figures Preface Introduction Part 1 . Maslov index in symplectic Banach spaces Chapter 1. General theory of symplectic analysis in Banach spaces 1.1. Dual pairs and double annihilators 1.2. Basic symplectic concepts 1.3. Natural decomposition of 𝑋 induced by a Fredholm pair of Lagrangian subspaces with vanishing index 1.4. Symplectic reduction of Fredholm pairs Chapter 2. The Maslov index in strong symplectic Hilbert space 2.1. The Maslov index via unitary generators 2.2. The Maslov index in finite dimensions 2.3. Properties of the Maslov index in strong symplectic Hilbert space Chapter 3. The Maslov index in Banach bundles over a closed interval 3.1. The Maslov index by symplectic reduction to a finite-dimensional subspace 3.2. Calculation of the Maslov index 3.3. Invariance of the Maslov index under symplectic operations 3.4. The Hörmander index Part 2 . Applications in global analysis Chapter 4. The desuspension spectral flow formula 4.1. Short account of predecessor formulae 4.2. Spectral flow for closed self-adjoint Fredholm relations 4.3. Symplectic analysis of operators and relations 4.4. Proof of the abstract spectral flow formula 4.5. An application: A general desuspension formula for the spectral flow of families of elliptic boundary value problems Backmatter Appendix A. Perturbation of closed subspaces in Banach spaces A.1. Some algebra facts A.2. The gap topology A.3. Continuity of operations of linear subspaces A.4. Smooth family of closed subspaces in Banach spaces A.5. Basic facts about symplectic Banach bundles A.6. Embedding Banach spaces A.7. Compact perturbations of closed subspaces Bibliography List of Symbols Index of Names/Authors Subject Index Back Cover