scholarly journals Notes on the subspace perturbation problem for off-diagonal perturbations

2016 ◽  
Vol 144 (9) ◽  
pp. 3825-3832 ◽  
Author(s):  
Albrecht Seelmann
Keyword(s):  
Perturbation Problem ◽  
Subspace Perturbation Problem

The length metric on the set of orthogonal projections and new estimates in the subspace perturbation problem

2015 ◽  
Vol 2015 (708) ◽  
pp. 1-15 ◽  
Author(s):  
Konstantin A. Makarov ◽  
Albrecht Seelmann
Keyword(s):  
Hilbert Space ◽  
Orthogonal Projections ◽  
Bounded Linear ◽  
Length Space ◽  
Metric Properties ◽  
Perturbation Problem ◽  
Subspace Perturbation Problem ◽  
Adjoint Operators ◽  
Spectral Subspaces ◽  
Operator Angle

AbstractWe consider the problem of variation of spectral subspaces for bounded linear self-adjoint operators in a Hilbert space. Using metric properties of the set of orthogonal projections as a length space, we obtain a new estimate on the norm of the operator angle associated with two spectral subspaces for isolated parts of the spectrum of the perturbed and unperturbed operators, respectively. In particular, recent results by Kostrykin, Makarov and Motovilov from [Proc. Amer. Math. Soc. 131, 3469–3476] and [Trans. Amer. Math. Soc. 359, 77–89] are strengthened.

scholarly journals On a subspace perturbation problem

2003 ◽  
Vol 131 (11) ◽  
pp. 3469-3476 ◽  
Author(s):  
Vadim Kostrykin ◽  
Konstantin A. Makarov ◽  
Alexander K. Motovilov
Keyword(s):  
Perturbation Problem ◽  
Subspace Perturbation Problem

A Existence Theory for Positive Solutions to Superlinear Repulsive Singular Differential Equations with Impulse Effects

2010 ◽  
Vol 40-41 ◽  
pp. 149-155
Author(s):  
Zhang Xiao Ying ◽  
Guan Li Hong
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Singular Perturbation ◽  
Positive Solutions ◽  
Existence Theory ◽  
Singular Differential Equations ◽  
Perturbation Problem ◽  
Nonlinear Alternative

In this paper, we study positive solutions to the repulsive singular perturbation Hill equations with impulse effects. It is proved that such a perturbation problem has at least one positive impulsive periodic solution by a nonlinear alternative of Leray--Schauder.

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