Notes on the subspace perturbation problem for off-diagonal perturbations

Seelmann, Albrecht

doi:10.1090/proc/13118

Notes on the subspace perturbation problem for off-diagonal perturbations
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Proc. Amer. Math. Soc. 144 (2016), 3825-3832 Request permission

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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