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The variation of spectral subspaces for linear self-adjoint operators underan additive bounded off-diagonal perturbation is studied. To this end, theoptimization approach for general perturbations in [J. Anal. Math., to appear;arXiv:1310.4360 (2013)] is adapted. It is shown that, in contrast to the caseof general perturbations, the corresponding optimization problem can not bereduced to a finite-dimensional problem. A suitable choice of the involvedparameters provides an upper bound for the solution of the optimizationproblem. In particular, this yields a rotation bound on the subspaces that isstronger than the previously known one from [J. Reine Angew. Math. (2013),DOI:10.1515/crelle-2013-0099].

Notes on the subspace perturbation problem for off-diagonal perturbations