Unbounded Fredholm Operators and Spectral Flow
| dc.creator | Booss-Bavnbek, Bernhelm | |
| dc.creator | Lesch, Matthias | |
| dc.creator | Phillips, John | |
| dc.date | 2001-08-02 | |
| dc.date | 2004-02-12 | |
| dc.date.accessioned | 2026-07-07T04:42:50Z | |
| dc.date.available | 2026-07-07T04:42:50Z | |
| dc.description | 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. | |
| dc.description | 23 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.identifier | https://arxiv.org/abs/math/0108014 | |
| dc.identifier | http://arxiv.org/abs/math/0108014 | |
| dc.identifier | Canadian Journal of Mathematics vol. 57, no.2 (2005), 225-250. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61956 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | Spectral Theory | |
| dc.subject | 58J30; 47A53; 19K56; 58J32 | |
| dc.title | Unbounded Fredholm Operators and Spectral Flow | |
| dc.type | text |