A new topology on the space of unbounded selfadjoint operators and the spectral flow

2006/07/30 by Charlotte Wahl, Wahl, Charlotte
Mathematics · #46L80 #47A53 #58J30 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #K-Theory and Homology (math.KT) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0607783

openalex publication_date 2006/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a new topology, weaker than the gap topology, on the space of selfadjoint unbounded operators on a separable Hilbert space. We show that the subspace of selfadjoint Fredholm operators represents the functor K¹ from the category of compact spaces to the category of abelian groups and prove a similar result for K⁰. We define the spectral flow of a continuous path of selfadjoint Fredholm operators generalizing the approach of Booss-Bavnek--Lesch--Phillips.

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