On the Pettis-Divisor Property for Dunford-Pettis Operators
Commun. Korean Math. Soc. 1998 Vol. 13, No. 4, 775-780
Sung-Jin Cho, Chun Kee Park
Pukyong National University, KangWon National University
Abstract : In this paper it is shown that Dunford-Pettis operators obey the ``Pettis-divisor property": if $T$ is a Dunford-Pettis operator from $L_1(\mu)$ to a Banach space $X$, then there is a non-Pettis representable operator $S:L_1(\mu)\lr L_1(\mu)$ such that $T\circ S$ is Pettis representable.
Keywords : Weak Radon-Nikodym property, nearly weak Radon-Nikodym property, Dunford-Pettis operators, Pettis representable, nearly Pettis representable
MSC numbers : 46B22
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