A Topological Approach to Unitary Spectral Flow via Continuous Enumeration of Eigenvalues

2015/02/09 by Nurulla Azamov, Azamov, Nurulla, Tom Daniels +3
Mathematics · #47A55 #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP) #math.FA #math.SP #msc:47A55

paper · pdf · doi:10.48550/arxiv.1502.02319

46 pages

arxiv created 2020/06/09 · arxiv updated 2020/06/11

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.

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