We introduce the new ideal of strongly -continuous linear operators in order to study the adjoints of the -absolutely continuous linear operators. Starting from this ideal we build a new multi-ideal by using the composition method. We prove the corresponding Pietsch domination theorem and we present a representation of this multi-ideal by a tensor norm. A factorization theorem characterizing the corresponding multi-ideal – which is also new for the linear case – is given. When applied to the case of the Cohen strongly -summing operators, this result gives also a new factorization theorem.