Notes on the subspace perturbation problem for off-diagonal perturbations
Abstract
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded off-diagonal perturbation is studied. To this end, the optimization approach for general perturbations in [J. Anal. Math., to appear; arXiv:1310.4360 (2013)] is adapted. It is shown that, in contrast to the case of general perturbations, the corresponding optimization problem can not be reduced to a finite-dimensional problem. A suitable choice of the involved parameters provides an upper bound for the solution of the optimization problem. In particular, this yields a rotation bound on the subspaces that is stronger than the previously known one from [J. Reine Angew. Math. (2013), DOI:10.1515/crelle-2013-0099].
Cite
@article{arxiv.1412.6294,
title = {Notes on the subspace perturbation problem for off-diagonal perturbations},
author = {Albrecht Seelmann},
journal= {arXiv preprint arXiv:1412.6294},
year = {2016}
}
Comments
8 pages; some editorial changes, two added references, some corrected typos