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.
CitationHo, K.-P. (2019). Interpolation of sublinear operators which map into Riesz spaces and applications. Proceedings of the American Mathematical Society, 147(8), 3479-3492. doi: 10.1090/proc/14506
- Riesz space
- Sublinear operators
- Hahn-Banach theorem for operators mapping into a complex Riesz space