This is an announcement for the paper “Interpolation of nonlinear positive or order preserving operators on Banach lattices” by Ralph Chillhttps://arxiv.org/search/math?searchtype=author&query=Chill%2C+R, Alberto Fiorenzahttps://arxiv.org/search/math?searchtype=author&query=Fiorenza%2C+A, Sebastian Krolhttps://arxiv.org/search/math?searchtype=author&query=Krol%2C+S.
Abstract: We study the relationship between exact interpolation spaces for positive, linear operators, for order preserving, Lipschitz continuous operators, and for positive Gagliardo-Peetre operators, and exact partially $K$-monotone spaces in interpolation couples of compatible Banach lattices. By general Banach lattice theory we recover a characterisation of exact interpolation spaces for order preserving, Lipschitz continuous operators in the couple $(L^1,L^\infty )$ due to Bénilan and Crandall.