The Maslov index and the spectral flow—revisited

Marek Izydorek; Joanna Janczewska; Nils Waterstraat

doi:10.1186/s13663-019-0655-6

The Maslov index and the spectral flow—revisited

Abstract

We give an elementary proof of a celebrated theorem of Cappell, Lee and Miller which relates the Maslov index of a pair of paths of Lagrangian subspaces to the spectral flow of an associated path of self-adjoint first-order operators. We particularly pay attention to the continuity of the latter path of operators, where we consider the gap-metric on the set of all closed operators on a Hilbert space. Finally, we obtain from Cappell, Lee and Miller’s theorem a spectral flow formula for linear Hamiltonian systems which generalises a recent result of Hu and Portaluri.

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Authors (3)

Marek Izydorek prof. dr hab.
Joanna Janczewska prof. dr hab.
Nils Waterstraat
- Institut für Mathematik, Naturwissenschaftliche Fakultät II, Martin-Luther-Universität Halle-Wittenberg, Halle (Saale), Germany

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Articles

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artykuły w czasopismach

Published in:

Fixed Point Theory and Applications no. 2019, pages 1 - 20,
ISSN: 1687-1820

Language:

English

Publication year:

2019

Bibliographic description:

Izydorek M., Janczewska J., Waterstraat N.: The Maslov index and the spectral flow—revisited// Fixed Point Theory and Applications -Vol. 2019, (2019), s.1-20

DOI: