Coincidence of extendible vector-valued ideals with their minimal kernel

We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if AA is an ideal of n  -linear mappings we give conditions for which the equality A(E1,…,En;F)=Amin(E1,…,En;F)A(E1,…,En;F)=Amin(E1,…,En;F) holds isometrically. As an application, we obtain in many cases that the monomials form a Schauder basis of the space A(E1,…,En;F)A(E1,…,En;F). Several structural and geometric properties are also derived using this equality. We apply our results to the particular case where AA is the classical ideal of extendible or Pietsch-integral multilinear operators. Similar statements are given for ideals of vector-valued homogeneous polynomials.