# [Banach] Abstract of a paper by Dumitru Popa

Dale Alspach alspach at www.math.okstate.edu
Thu Mar 22 06:49:15 CDT 2007

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 at univ-ovidius.ro

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http://front.math.ucdavis.edu/math.FA/0703626

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http://arXiv.org/abs/math.FA/0703626

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