Unbounded Fredholm Operators and Spectral Flow
By Bernhelm Booss-Bavnbek, M. Lesch, J. Phillips. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2001
135 citations recorded by the source corpus.
Abstract We study the gap (= “projection norm” = “graph distance”) topology of the space of all (not necessarily bounded) self-adjoint Fredholm operators in a separable Hilbert space by the Cayley transform and direct methods. In particular, we show the surprising result that this space is connected in contrast 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.
Subfields: Applied Mathematics, Computational Theory and Mathematics
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In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- Dixmier traces and some applications in non-commutative geometry (2006, background): “In this section our object is to describe the classes of positive Connes–Dixmier-measurable operators and positive Dixmier-measurable operators and to show that these two classes actually coincide.”