2,281 research outputs found
Perturbation of spectra and spectral subspaces
We consider the problem of variation of spectral subspaces for linear
self-adjoint operators under off-diagonal perturbations. We prove a number of
new optimal results on the shift of the spectrum and obtain (sharp) estimates
on the norm of the difference of two spectral projections
On a Subspace Perturbation Problem
We discuss the problem of perturbation of spectral subspaces for linear
self-adjoint operators on a separable Hilbert space. Let and be bounded
self-adjoint operators. Assume that the spectrum of consists of two
disjoint parts and such that . We show that the norm of the difference of the spectral projections
\EE_A(\sigma) and \EE_{A+V}\big (\{\lambda | \dist(\lambda, \sigma)
for and is less then one whenever either (i)
or (ii) and certain assumptions on the
mutual disposition of the sets and are satisfied
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