Stability and instability of weighted composition operators
| dc.creator | Araujo, Jesus | |
| dc.creator | Font, Juan J. | |
| dc.date | 2008-01-16 | |
| dc.date.accessioned | 2026-07-07T08:54:49Z | |
| dc.date.available | 2026-07-07T08:54:49Z | |
| dc.description | Let $ε>0$. A continuous linear operator $T:C(X) \ra C(Y)$ is said to be {\em $ε$-disjointness preserving} if $\vc (Tf)(Tg)\vd_{\infty} \le ε$, whenever $f,g\in C(X)$ satisfy $\vc f\vd_{\infty} =\vc g\vd_{\infty} =1$ and $fg\equiv 0$. In this paper we address basically two main questions: 1.- How close there must be a weighted composition operator to a given $ε$-disjointness preserving operator? 2.- How far can the set of weighted composition operators be from a given $ε$-disjointness preserving operator? We address these two questions distinguishing among three cases: $X$ infinite, $X$ finite, and $Y$ a singleton ($ε$-disjointness preserving functionals). We provide sharp stability and instability bounds for the three cases. | |
| dc.description | 37 pages, 7 figures. A beamer presentation at http://www.araujo.tk | |
| dc.identifier | https://arxiv.org/abs/0801.2477 | |
| dc.identifier | http://arxiv.org/abs/0801.2477 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146077 | |
| dc.subject | Functional Analysis | |
| dc.subject | Primary 47B38; Secondary 46J10, 47B33 | |
| dc.title | Stability and instability of weighted composition operators | |
| dc.type | text |