We present a characterization of Banach function lattices with the Fatou property generated by the interpolation sum applied to infinite families of Banach lattices with the Fatou property. We also discuss the Köthe duality between the sum and the intersection constructions for Banach spaces.
"Banach lattice sums with hereditary Fatou properties." Funct. Approx. Comment. Math. 50 (2) 271 - 282, June 2014. https://doi.org/10.7169/facm/2014.50.2.5