Unbounded Fredholm Operators and Spectral Flow

dc.creatorBooss-Bavnbek, Bernhelm
dc.creatorLesch, Matthias
dc.creatorPhillips, John
dc.date2001-08-02
dc.date2004-02-12
dc.date.accessioned2026-07-07T04:42:50Z
dc.date.available2026-07-07T04:42:50Z
dc.descriptionWe 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.
dc.description23 pages, 2 figures; 09/10/2001 minor corrections, Proposition characterizing the range of the Riesz transformation added; 02/12/2004 very final version 1.0.2, minor corrections
dc.identifierhttps://arxiv.org/abs/math/0108014
dc.identifierhttp://arxiv.org/abs/math/0108014
dc.identifierCanadian Journal of Mathematics vol. 57, no.2 (2005), 225-250.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61956
dc.subjectFunctional Analysis
dc.subjectOperator Algebras
dc.subjectSpectral Theory
dc.subject58J30; 47A53; 19K56; 58J32
dc.titleUnbounded Fredholm Operators and Spectral Flow
dc.typetext

Files

Collections