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Positivity

pp 1–26 | Cite as

Interpolation of nonlinear positive or order preserving operators on Banach lattices

  • Ralph ChillEmail author
  • Alberto Fiorenza
  • Sebastian Król
Article

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.

Keywords

Nonlinear interpolation Exact interpolation spaces Order preserving operators Positive Gagliardo–Peetre operators Normal spaces 

Mathematics Subject Classification

Primary 46B42 46B70 47H07 Secondary 47H20 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institut für Analysis, Fakultät für MathematikTU DresdenDresdenGermany
  2. 2.Dipartimento di ArchitetturaUniversitá di Napoli Federico IINaplesItaly
  3. 3.Istituto per le Applicazioni del Calcolo “Mauro Picone”, sezione di NapoliConsiglio Nazionale delle RicercheNaplesItaly
  4. 4.Faculty of Mathematics and Computer ScienceNicolaus Copernicus UniversityToruńPoland

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