Journal of Operator Theory
Volume 81, Issue 2, Spring 2019 pp. 321-333.
Semidefinite perturbations in the subspace perturbation problem
Authors:
Albrecht Seelmann
Author institution:Fakultaet fuer Mathematik, Technische Universitaet Dortmund, Dortmund, D-44221, Germany
Summary: The variation of spectral subspaces for linear self-adjoint operators under an additive bounded semidefinite perturbation is
considered. A variant of the Davis-Kahan $\sin2\Theta$ theorem adapted to this situation is proved. Under a certain additional
geometric assumption on the separation of the spectrum of the unperturbed operator, this leads to a sharp estimate on the norm of
the difference of the spectral projections associated with isolated components of the spectrum of the perturbed and unperturbed
operators, respectively. Without this additional geometric assumption on the isolated components of the spectrum of the unperturbed
operator, a corresponding estimate is obtained by transferring a known optimization approach for general perturbations to the
present situation.
DOI: http://dx.doi.org/10.7900/jot.2018feb07.2186
Keywords: subspace perturbation problem, spectral subspaces, maximal angle between closed subspaces, semidefinite perturbations
Contents
Full-Text PDF