On a Subspace Perturbation Problem

Details On a Subspace Perturbation Problem On a Subspace Perturbation Problem

2002-03-22

arxiv.org/abs/math/0203240v3

Proc. Amer. Math. Soc. 131 (2003), 3469 - 3476

Mathematics

Spectral Theory

Scientific paper

10.1090/S0002-9939-03-06917-X

We discuss the problem of perturbation of spectral subspaces for linear self-adjoint operators on a separable Hilbert space. Let $A$ and $V$ be bounded self-adjoint operators. Assume that the spectrum of $A$ consists of two disjoint parts $\sigma$ and $\Sigma$ such that $d=\text{dist}(\sigma, \Sigma)>0$. We show that the norm of the difference of the spectral projections $\EE_A(\sigma)$ and $\EE_{A+V}\big (\{\lambda | \dist(\lambda, \sigma)$ $

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