Basic Functional Analysis Puzzles of Spectral Flow

Abstract

We explain an array of basic functional analysis puzzles on the way to general spectral flow formulae and indicate a direction of future topological research for dealing with these puzzles.

11 pages. Contribution to the Conference on "Geometry and Quantum Field Theory", Max Planck Institute for Mathematics, Bonn, June 20-26, 2010. Dedicated to Alan L. Carey on his 60th birthday

References in corpus (10)

• Quadratic estimates and functional calculi of perturbed Dirac operators
• The Calderon Projection: New Definition and Applications
• Index, eta and rho-invariants on foliated bundles
• The invertible double of elliptic operators
• General Spectral Flow Formula for Fixed Maximal Domain
• The Maslov index in weak symplectic functional analysis
• Weak Symplectic Functional Analysis and General Spectral Flow Formula
• Mathematical knowledge: internal, social and cultural aspects
• Perturbation of Sectorial Projections of Elliptic Pseudo-differential Operators
• Eigenvalue distribution for non-self-adjoint operators on compact manifolds with small multiplicative random perturbations

Cited by in corpus (2)

• Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of the metric
• Perturbation of Sectorial Projections of Elliptic Pseudo-differential Operators