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On the Witten index in terms of spectral shift functions

Carey, Alan; Gesztesy, Fritz; Potapov, Denis; Sukochev, Fedor A; Tomilov, Yuri


We study the model operator DA = (d/dt) + A in L2(R;H) associated with the operator path {A(t)}t=−∞∞, where (Af)(t) = A(t)f(t) for a.e. t ∈ R, and appropriate f ∈ L2(R;H) (with H a separable, complex Hilbert space). Denoting by A± the norm resolvent limits of A(t) as t → ±∞, our setup permits A(t) in H to be an unbounded, relatively trace class perturbation of the unbounded self-adjoint operator A-, and no discrete spectrum assumptions are made on A±. Introducing H1 = DA*DA, H2 = DADA*, the...[Show more]

CollectionsANU Research Publications
Date published: 2017
Type: Journal article
Source: Journal d'Analyse Mathematique
DOI: 10.1007/s11854-017-0003-x


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