A Topological Approach to Unitary Spectral Flow via Continuous Enumeration of Eigenvalues
Functional Analysis
2020-06-11 v2 Spectral Theory
Abstract
It is a well-known result of T.\,Kato that given a continuous path of square matrices of a fixed dimension, the eigenvalues of the path can be chosen continuously. In this paper, we give an infinite-dimensional analogue of this result, which naturally arises in the context of the so-called unitary spectral flow. This provides a new approach to spectral flow, which seems to be missing from the literature. It is the purpose of the present paper to fill in this gap.
Keywords
Cite
@article{arxiv.1502.02319,
title = {A Topological Approach to Unitary Spectral Flow via Continuous Enumeration of Eigenvalues},
author = {Nurulla Azamov and Tom Daniels and Yohei Tanaka},
journal= {arXiv preprint arXiv:1502.02319},
year = {2020}
}
Comments
46 pages