# Spectral shift for relative Schatten class perturbations

@inproceedings{Nuland2021SpectralSF, title={Spectral shift for relative Schatten class perturbations}, author={Teun D.H. van Nuland and Anna Skripka}, year={2021} }

. We aﬃrmatively settle the question on existence of a real-valued higher order spectral shift function for a pair of self-adjoint operators H and V such that V is bounded and V ( H − iI ) − 1 belongs to a Schatten-von Neumann ideal S n of compact operators in a separable Hilbert space. We also show that the function satisﬁes the same trace formula as in the known case of V ∈ S n and that it is unique up to a polynomial summand of order n − 1. Our result signiﬁcantly advances earlier partial…

## 3 Citations

### Spectral shift for resolvent comparable perturbations

- Mathematics
- 2022

Given a pair of self-adjoint operators H and V such that V is bounded and ( H + V − i ) − 1 − ( H − i ) − 1 belongs to the Schatten-von Neumann ideal S n , n ≥ 2, of operators on a separable Hilbert…

### Higher-order spectral shift function for resolvent comparable perturbations

- Mathematics
- 2022

Given a pair of self-adjoint operators H and V such that V is bounded and ( H + V − i ) − 1 − ( H − i ) − 1 belongs to the Schatten-von Neumann ideal S n , n ≥ 2, of operators on a separable Hilbert…

### Cyclic cocycles and one-loop corrections in the spectral action

- Mathematics
- 2022

. We present an intelligible review of recent results concerning cyclic cocycles in the spectral action and one-loop quantization. We show that the spectral action, when perturbed by a gauge…

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