Khinchin's inequality, Dunford--Pettis and compact operators on the space $\pmb{C([0,1],X)}$
| dc.creator | Popa, Dumitru | |
| dc.date | 2007-03-21 | |
| dc.date.accessioned | 2026-07-07T07:53:05Z | |
| dc.date.available | 2026-07-07T07:53:05Z | |
| dc.description | We prove that if $X,Y$ are Banach spaces, $Ω$ a compact Hausdorff space and $U\hbox{\rm :} C(Ω,X)\to Y$ is a bounded linear operator, and if $U$ is a Dunford--Pettis operator the range of the representing measure $G(Σ) \subseteq DP(X,Y)$ is an uniformly Dunford--Pettis family of operators and $\|G\|$ is continuous at $\emptyset$. As applications of this result we give necessary and/or sufficient conditions that some bounded linear operators on the space $C([0,1],X)$ with values in $c_{0}$ or $l_{p}$, ($1\leq p<\infty$) be Dunford--Pettis and/or compact operators, in which, Khinchin's inequality plays an important role. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703626 | |
| dc.identifier | http://arxiv.org/abs/math/0703626 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126117 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B28; 47A80; 47B10 | |
| dc.title | Khinchin's inequality, Dunford--Pettis and compact operators on the space $\pmb{C([0,1],X)}$ | |
| dc.type | text |