ON THE PETTIS-DIVISOR PROPERTY FOR DUNFORD-PETTIS OPERATORS

  • SUNG-JIN CHO (Department of Applied Mathematics Pukyong National University) ;
  • CHUN KEE PARK (Department of Mathematics KangWon National University)
  • Published : 1998.10.01

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 : $L_1$($\mu$)longrightarrow$L_1$($\mu$) such that To S is Pettis representable.