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Notes on the subspace perturbation problem for off-diagonal perturbations

Albrecht Seelmann

subject

Pure mathematicsOptimization problemApplied MathematicsGeneral MathematicsDiagonalPerturbation (astronomy)Upper and lower boundsLinear subspaceFunctional Analysis (math.FA)Mathematics - Spectral TheoryMathematics - Functional AnalysisBounded functionFOS: Mathematics47A55 (Primary) 47A15 47B15 (Secondary)Spectral Theory (math.SP)Subspace topologyMathematics

description

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].

yearjournalcountryeditionlanguage
2014-12-19
10.1090/proc/13118http://arxiv.org/abs/1412.6294