Operators on separable L1-predual spaces

We give an extension of the classical Bartle–Dunford–Schwartz theorem for weakly compact operators on a $C(K)$ space, to weakly compact operators on a separable $L^1$-predual space. Using this we show that for operators on these spaces, the set of weakly compact operators that attain their norm is dense in the space of weakly compact operators. For operators from the space of affine continuous functions on a metrizable Choquet simplex with values in an uniformly convex space, we show that the operator theoretic version of the Bishop–Phelps–Bollobás property is valid. This gives an extension of some recent work of Kim and Lee.