Nuclear operators on spaces of continuous vector-valued functions
| dc.creator | Saab, Paulette | |
| dc.creator | Smith, Brenda | |
| dc.date | 1990-03-27 | |
| dc.date.accessioned | 2026-07-07T09:14:40Z | |
| dc.date.available | 2026-07-07T09:14:40Z | |
| dc.description | Let $Ω$ be a compact Hausdorff space, let $E$ be a Banach space, and let $C(Ω, E)$ stand for the Banach space of all $E$-valued continuous functions on $Ω$ under supnorm. In this paper we study when nuclear operators on $C(Ω, E)$ spaces can be completely characterized in terms of properties of their representing vector measures. We also show that if $F$ is a Banach space and if $T:\ C(Ω, E)\rightarrow F$ is a nuclear operator, then $T$ induces a bounded linear operator $T^\#$ from the space $C(Ω)$ of scalar valued continuous functions on $Ω$ into $\slN(E,F)$ the space of nuclear operators from $E$ to $F$, in this case we show that $E^*$ has the Radon-Nikodym property if and only if $T^\#$ is nuclear whenever $T$ is nuclear. | |
| dc.identifier | https://arxiv.org/abs/math/9201211 | |
| dc.identifier | http://arxiv.org/abs/math/9201211 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152757 | |
| dc.subject | Functional Analysis | |
| dc.subject | Primary 46E40, 46G10, 47B10, Secondary 28B05, 28B20 | |
| dc.title | Nuclear operators on spaces of continuous vector-valued functions | |
| dc.type | text |