Some ideals of operators between spaces of operators

Abstract

For A ∈ L(X, Y ), B ∈ L(Z , T ) we consider the operator

h : L(Y, Z ) →L(X, T ), h(U ) = BU A.

We prove that in some hypotheses about A and B the operator h is in some ideal of operators. As a consequence we obtain that the ideals of Dunford-Pettis dual operator and weak∗ -norm sequentially continuous operators are projective tensor stable, Nc^dual ⊗_π D P^dual ⊂ Nc^dual , G P^dual ⊗_π D P^dual ⊂ G P^dual.