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On a spectral flow formula for the homological index

Carey, Alan; Grosse, Harald; Kaad, Jens


Consider a selfadjoint unbounded operator D on a Hilbert space H and a one parameter norm continuous family of selfadjoint bounded operators {A(t) | t ∈ R} that converges in norm to asymptotes A± at ±∞. Then under certain conditions [22] that include the assumption that the operators {D(t) = D + A(t),t ∈ R} all have discrete spectrum the spectral flow along the path {D(t)} can be shown to be equal to the index of ∂t + D(t) when the latter is an unbounded Fredholm operator on L2(R, H). In [16]...[Show more]

CollectionsANU Research Publications
Date published: 2016
Type: Journal article
Source: Advances in Mathematics
DOI: 10.1016/j.aim.2015.10.030


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