The Uniqueness of the Spectral Flow on Spaces of Unbounded Self – adjoint Fredholm Operators

@inproceedings{Lesch2004TheUO,
title={The Uniqueness of the Spectral Flow on Spaces of Unbounded Self – adjoint Fredholm Operators},
author={Matthias Lesch},
year={2004}
}

We discuss several natural metrics on spaces of unbounded self– adjoint operators and their relations, among them the Riesz and the graph metric. We show that the topologies of the spaces of Fredholm operators resp. invertible operators depend heavily on the metric. Nevertheless we prove that in all cases the spectral flow is up to a normalization the only integer invariant of non–closed paths which is path additive and stable under homotopies with endpoints varying in the space of invertible… CONTINUE READING