  We analyze the interplay between maximal/minimal/adjoint ideals of
multilinear operators (between sequence spaces) and their associated K\"othe
sequence spaces. We establish relationships with spaces of multipliers and
apply these results to describe diagonal multilinear operators from Lorentz
sequence spaces. We also define and study some properties of the ideal of
$(E;p)$-summing multilinear mappings, a natural extension of the linear ideal
of absolutely $(E;p)$-summing operators.
