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Unbounded Fredholm Operators and Spectral Flow

Bernhelm Booss-Bavnbek·Matthias Lesch·John Phillips
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Abstract

We study the gap (= "projection norm" = "graph distance") topology of the space of (not necessarily bounded) self--adjoint Fredholm operators in a separable Hilbert space by the Cayley transform and direct methods. In particular, we show that the space is connected contrary to the bounded case. Moreover, we present a rigorous definition of spectral flow of a path of such operators (actually alternative but mutually equivalent definitions) and prove the homotopy invariance. As an example, we discuss operator curves on manifolds with boundary.

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Bernhelm Booss-Bavnbek, Matthias Lesch, John Phillips. 2004-02-12. Unbounded Fredholm Operators and Spectral Flow. https://arxiv.org/abs/math/0108014

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