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arXiv · 1502.02319

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

Nurulla Azamov·Tom Daniels·Yohei Tanaka
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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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Nurulla Azamov, Tom Daniels, Yohei Tanaka. 2020-06-09. A Topological Approach to Unitary Spectral Flow via Continuous Enumeration of Eigenvalues. https://arxiv.org/abs/1502.02319

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