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.References
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Additional Information
- Kwok-Pun Ho
- Affiliation: Department of Mathematics and Information Technology, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, Hong Kong, People’s Republic of China
- MR Author ID: 723414
- Email: vkpho@eduhk.hk
- Received by editor(s): September 6, 2018
- Received by editor(s) in revised form: November 27, 2018, and December 4, 2018
- Published electronically: April 8, 2019
- Communicated by: Stephen Dilworth
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3479-3492
- MSC (2010): Primary 46B70, 46A40, 42B25
- DOI: https://doi.org/10.1090/proc/14506
- MathSciNet review: 3981126