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Interpolation of sublinear operators which map into Riesz spaces and applications


Author: Kwok-Pun Ho
Journal: Proc. Amer. Math. Soc. 147 (2019), 3479-3492
MSC (2010): Primary 46B70, 46A40, 42B25
DOI: https://doi.org/10.1090/proc/14506
Published electronically: April 8, 2019
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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.


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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
Email: vkpho@eduhk.hk

DOI: https://doi.org/10.1090/proc/14506
Keywords: Riesz space, interpolation, sublinear operators, Hahn-Banach theorem for operators mapping into a complex Riesz space
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
Article copyright: © Copyright 2019 American Mathematical Society