Unbounded Fredholm Operators and Spectral Flow
泛函分析
2007-05-23 v3 算子代数
谱理论
摘要
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.
引用
@article{arxiv.math/0108014,
title = {Unbounded Fredholm Operators and Spectral Flow},
author = {Bernhelm Booss-Bavnbek and Matthias Lesch and John Phillips},
journal= {arXiv preprint arXiv:math/0108014},
year = {2007}
}
备注
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