Signature and spectral flow of \(J\)-unitary \(\mathbb S^1\)-Fredholm operators

DOI10.1007/s00020-013-2094-9zbMath1325.47084arXiv1210.0184OpenAlexW2042109852MaRDI QIDQ2445449

Hermann Schulz-Baldes

Publication date: 14 April 2014

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.0184

zbMATH Keywords

Krein spaceFredholm operatorLagrangian subspaceintersection index\(J\)-unitary operator

Mathematics Subject Classification ID

(Semi-) Fredholm operators; index theories (47A53) Lagrangian submanifolds; Maslov index (53D12) Spectral flows (58J30) Linear operators on spaces with an indefinite metric (47B50)

Related Items (6)

Dimensional reduction and scattering formulation for even topological invariants ⋮ Topological edge states for disordered bosonic systems ⋮ On the Fredholm Lagrangian Grassmannian, spectral flow and ODEs in Hilbert spaces ⋮ Analyticity properties of the scattering matrix for matrix Schrödinger operators on the discrete line ⋮ Spectral flow of monopole insertion in topological insulators ⋮ Oscillation Theory for the Density of States of High Dimensional Random Operators

Cites Work

• Topological invariants of edge states for periodic two-dimensional models
• Fredholm-Lagrangian-Grassmannian and the Maslov index
• Sturm intersection theory for periodic Jacobi matrices and linear Hamiltonian systems
• The index of a pair of projections
• Computation of the Maslov index and the spectral flow via partial signatures.
• Zur Spektraltheorie J-selbstadjungierter Operatoren
• On the iteration of closed geodesics and the sturm intersection theory
• On linear-fractional transformations with operator coefficients
• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
• Signatures for ‐hermitians and ‐unitaries on Krein spaces with Real structures
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