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arXiv · 1810.09684

Interpolation of nonlinear positive or order preserving operators on Banach lattices

Ralph Chill·Alberto Fiorenza·Sebastian Krol
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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 B\'enilan and Crandall.

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Ralph Chill, Alberto Fiorenza, Sebastian Krol. 2018-10-23. Interpolation of nonlinear positive or order preserving operators on Banach lattices. https://arxiv.org/abs/1810.09684

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