On a Subspace Perturbation Problem
| dc.creator | Kostrykin, Vadim | |
| dc.creator | Makarov, Konstantin A. | |
| dc.creator | Motovilov, Alexander K. | |
| dc.date | 2002-03-22 | |
| dc.date | 2002-06-27 | |
| dc.date.accessioned | 2026-07-07T04:47:15Z | |
| dc.date.available | 2026-07-07T04:47:15Z | |
| dc.description | 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 $σ$ and $Σ$ such that $d=\text{dist}(σ, Σ)>0$. We show that the norm of the difference of the spectral projections $\EE_A(σ)$ and $\EE_{A+V}\big (\{λ| \dist(λ, σ)$ $<d/2\}\big)$ for $A$ and $A+V$ is less then one whenever either (i) $\|V\|<\frac{2}{2+π}d$ or (ii) $\|V\|<{1/2}d$ and certain assumptions on the mutual disposition of the sets $σ$ and $Σ$ are satisfied. | |
| dc.identifier | https://arxiv.org/abs/math/0203240 | |
| dc.identifier | http://arxiv.org/abs/math/0203240 | |
| dc.identifier | Proc. Amer. Math. Soc. 131 (2003), 3469 - 3476 | |
| dc.identifier | doi:10.1090/S0002-9939-03-06917-X | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63639 | |
| dc.subject | Spectral Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Primary 47A55, 47A15; Secondary 47B15 | |
| dc.title | On a Subspace Perturbation Problem | |
| dc.type | text |