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Author Booss, Bernhelm, 1941- author.

Title The Maslov index in symplectic Banach spaces / Bernhelm Booß-Bavnbek, Chaofeng Zhu
Published Providence, RI : American Mathematical Society, [2018]
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Description 1 online resource (x, 118 pages) : illustrations
Series Memoirs of the American Mathematical Society, 0065-9266 ; volume 252, number 1201
Memoirs of the American Mathematical Society ; no. 1201
Contents 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
Summary "We consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying weak symplectic structures. Assuming vanishing index, we obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using such decompositions we define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. We 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, we 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, we 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."--Page v
Notes "March 2018, volume 252, number 1201 (second of 6 numbers)."
Bibliography Includes bibliographical references (pages 103-107) and indexes
Notes Print version record
Subject Banach spaces.
Maslov index.
Symplectic spaces.
Banach spaces.
MATHEMATICS -- Geometry -- General.
Maslov index.
Symplectic spaces.
Form Electronic book
Author Zhu, Chaofeng, 1973- author.
American Mathematical Society, publisher.
ISBN 1470443716