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Notes on the subspace perturbation problem for off-diagonal perturbations


Author: Albrecht Seelmann
Journal: Proc. Amer. Math. Soc. 144 (2016), 3825-3832
MSC (2010): Primary 47A55; Secondary 47A15, 47B15
DOI: https://doi.org/10.1090/proc/13118
Published electronically: April 13, 2016
MathSciNet review: 3513541
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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 cannot 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. 708 (2015), 1-15].


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Additional Information

Albrecht Seelmann
Affiliation: FB 08 - Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, D-55099 Mainz, Germany
Email: seelmann@mathematik.uni-mainz.de

DOI: https://doi.org/10.1090/proc/13118
Keywords: Subspace perturbation problem, spectral subspaces, maximal angle between closed subspaces, off-diagonal perturbations
Received by editor(s): October 26, 2015
Published electronically: April 13, 2016
Communicated by: Michael Hitrik
Article copyright: © Copyright 2016 American Mathematical Society

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