This is an announcement for the paper "Khinchin's inequality, Dunford--Pettis and compact operators on the space $\pmb{C([0,1],X)}$" by Dumitru Popa.
Abstract: We prove that if $X,Y$ are Banach spaces, $\Omega$ a compact Hausdorff space and $U\hbox{\rm :}\ C(\Omega,X)\rightarrow Y$ is a bounded linear operator, and if $U$ is a Dunford--Pettis operator the range of the representing measure $G(\Sigma) \subseteq DP(X,Y)$ 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.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B28; 47A80; 47B10
Remarks: 18 pages
The source file(s), mat01.cls: 37299 bytes, mathtimy.sty: 20 bytes, pm2710new.tex: 66481 bytes, is(are) stored in gzipped form as 0703626.tar.gz with size 24kb. The corresponding postcript file has gzipped size 76kb.
Submitted from: dpopa@univ-ovidius.ro
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