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BMV conjecture and positivity of spectral shift for relatively Schatten perturbations
Abstract
We establish BMV-type results and prove the positivity-preserving property and uniqueness of support-normalized spectral shift functions of arbitrary order for semibounded operators with relatively Schatten-von Neumann perturbations. We also derive correlation inequalities in the relative Hilbert-Schmidt case. These results build on a new positivity-preserving property for the trace of a higher-order operator derivative along a relatively Schatten direction and are obtained using methods of multilinear operator integration and approximation.
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BibTeX
@misc{pradhan2026conjecture,
title = {{BMV conjecture and positivity of spectral shift for relatively Schatten perturbations}},
author = {Chandan Pradhan and Anna Skripka},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05879},
eprint = {2611.05879},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05879},
}
RIS
TY - UNPB
TI - BMV conjecture and positivity of spectral shift for relatively Schatten perturbations
AU - Chandan Pradhan
AU - Anna Skripka
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.05879
UR - https://arxiv.org/abs/2611.05879
AB - We establish BMV-type results and prove the positivity-preserving property and uniqueness of support-normalized spectral shift functions of arbitrary order for semibounded operators with relatively Schatten-von Neumann perturbations. We also derive correlation inequalities in the relative Hilbert-Schmidt case. These results build on a new positivity-preserving property for the trace of a higher-order operator derivative along a relatively Schatten direction and are obtained using methods of multilinear operator integration and approximation.
ER -