Weakly compact linear operators on space of Dunford integral function

Abstract

Abstract This study discussed the integral of Dunford and compact linear operator on space of Dunford integral function. For each f which is Dunford integral on [a,b] is defined as an operator DL by DL (x *) = x * f, for each x * ∈ X * This study resulted that the operator DL is both a continuous linear operator and weakly compact operators. Then, it was defined as the adjoint of the operator D L * by D L * ( h ) ( x * ) = ∫ a b h D L ( x * ) each h ∈ (L 1)* The adjoint operator D L * is continuous and weakly compact linear operators.