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

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

2006-07-30

arxiv.org/abs/math/0607783v2

Mathematics

Functional Analysis

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

Scientific paper

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.

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