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Beschreibung:
We present conditions for a family (A(x))x∞Rd of self-adjoint operators in H r = Cr ⊗ H for a separable complex Hilbert space H, such that the Callias operator D = ic∇ + A(X) satisfies that (D*D + 1)−N − (DD* + 1)−N is trace class in L2(Rd, H r ). Here, c∇ is the Dirac operator associated to a Clifford multiplication c of rank r on Rd , and A(X) is fibre-wise multiplication with A(x) in L2(Rd, H r).