Diagonal multilinear operators on Kothe sequence spaces

We analyse the interplay between maximal/minimal/adjoint ideals of multilinear operators (between sequence spaces) and their associated Kothe 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.