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

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.

preprint2020arXivOpen access
Nurulla AzamovTom DanielsYohei Tanaka
math.FAmath.SP
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Nurulla AzamovTom DanielsYohei Tanaka

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