Functions of perturbed operators
| dc.creator | Aleksandrov, A. B. | |
| dc.creator | Peller, V. V. | |
| dc.date | 2009-04-10 | |
| dc.date.accessioned | 2026-07-07T13:03:15Z | |
| dc.date.available | 2026-07-07T13:03:15Z | |
| dc.description | We prove that if $0<\a<1$ and $f$ is in the Hölder class $Ł_\a(\R)$, then for arbitrary self-adjoint operators $A$ and $B$ with bounded $A-B$, the operator $f(A)-f(B)$ is bounded and $\|f(A)-f(B)\|\le\const\|A-B\|^\a$. We prove a similar result for functions $f$ of the Zygmund class $Ł_1(\R)$: $\|f(A+K)-2f(A)+f(A-K)\|\le\const\|K\|$, where $A$ and $K$ are self-adjoint operators. Similar results also hold for all Hölder-Zygmund classes $Ł_\a(\R)$, $\a>0$. We also study properties of the operators $f(A)-f(B)$ for $f\inŁ_\a(\R)$ and self-adjoint operators $A$ and $B$ such that $A-B$ belongs to the Schatten--von Neumann class $\bS_p$. We consider the same problem for higher order differences. Similar results also hold for unitary operators and for contractions. | |
| dc.description | 6 pages | |
| dc.identifier | https://arxiv.org/abs/0904.1760 | |
| dc.identifier | http://arxiv.org/abs/0904.1760 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226730 | |
| dc.subject | Functional Analysis | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.subject | Spectral Theory | |
| dc.subject | 47A55, 47B49, 47A60 | |
| dc.title | Functions of perturbed operators | |
| dc.type | text |