English

A new topology on the space of unbounded selfadjoint operators and the spectral flow

Functional Analysis 2007-05-23 v2 K-Theory and Homology

Abstract

We define a new topology, weaker than the gap topology, on the space of selfadjoint unbounded operators on a separable Hilbert space. We show that the subspace of selfadjoint Fredholm operators represents the functor K1K^1 from the category of compact spaces to the category of abelian groups and prove a similar result for K0K^0. We define the spectral flow of a continuous path of selfadjoint Fredholm operators generalizing the approach of Booss-Bavnek--Lesch--Phillips.

Keywords

Cite

@article{arxiv.math/0607783,
  title  = {A new topology on the space of unbounded selfadjoint operators and the spectral flow},
  author = {Charlotte Wahl},
  journal= {arXiv preprint arXiv:math/0607783},
  year   = {2007}
}

Comments

13 pages, Def. of Dom D corrected and minor corrections, more detailed exposition