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Interpolation of nonlinear positive or order preserving operators on Banach lattices (1810.09684v1)
Published 23 Oct 2018 in math.FA
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 $(L1,L\infty )$ due to B\'enilan and Crandall.