Perturbations of APS Boundary Conditions for Lorentzian Dirac Operators
Lennart Ronge
TL;DR
This paper investigates the stability of Atiyah-Patodi-Singer (APS) boundary conditions for Lorentzian Dirac operators under perturbations, establishing criteria for maintaining Fredholm properties.
Contribution
It develops criteria for perturbing APS boundary conditions without losing the Fredholm property of Lorentzian Dirac operators.
Findings
Criteria for perturbing boundary conditions while preserving Fredholmness
Characterization of Fredholm pairs of projections in this context
Conditions under which perturbations do not destroy operator stability
Abstract
We study how far APS boundary conditions for a Lorentzian Dirac operator may be perturbed without destroying Fredholmness of the Dirac operator. This is done by developing criteria under which the perturbation of a compact pair of projections is a Fredholm pair.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Advanced Operator Algebra Research · Algebraic and Geometric Analysis