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

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 $K^1$ from the category of compact spaces to the category of abelian groups and prove a similar result for $K^0$. We define the spectral flow of a continuous path of selfadjoint Fredholm operators generalizing the approach of Booss-Bavnek--Lesch--Phillips.

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

Cited by in corpus (1)

• On the noncommutative spectral flow