Interpolation of sublinear operators which map into Riesz spaces and applications

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Abstract

We establish an interpolation result for sublinear operators which map into Riesz spaces. This result applies to all interpolation functors including the real interpolation and the complex interpolation. One component of our proof which may be of independent interest is the perhaps already known fact that the generalized versions of the Hahn-Banach theorem due to L. V. Kantorovich and M. M. Day also hold for complex vector spaces. Copyright © 2019 American Mathematical Society.
Original languageEnglish
Pages (from-to)3479-3492
JournalProceedings of the American Mathematical Society
Volume147
Issue number8
Early online date08 Apr 2019
DOIs
Publication statusE-pub ahead of print - 08 Apr 2019

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Sublinear Operator
Riesz Space
Mathematical operators
Interpolation
Interpolate
Hahn-Banach Theorem
Complex Interpolation
Real Interpolation
Functor
Vector space
Vector spaces

Bibliographical note

Ho, K.-P. (2019). Interpolation of sublinear operators which map into Riesz spaces and applications. Proceedings of the American Mathematical Society. Advance online publication. doi: 10.1090/proc/14506

Keywords

  • Riesz space
  • Interpolation
  • Sublinear operators
  • Hahn-Banach theorem for operators mapping into a complex Riesz space