A New Topology on the Space of Unbounded Selfadjoint Operators, K-theory and Spectral Flow
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.
KeywordsSpectral flow classifying space K-theory unbounded operators
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