Uniform homeomorphisms between spheres induced by interpolation methods
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- by Willian Corrêa;
- Proc. Amer. Math. Soc. 152 (2024), 2157-2167
- DOI: https://doi.org/10.1090/proc/16730
- Published electronically: March 20, 2024
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Abstract:
M. Daher [Canad. Math. Bull. 38 (1995), pp. 286–294] showed that if $(X_0, X_1)$ is a regular couple of uniformly convex spaces then the unit spheres of the complex interpolation spaces $X_{\theta }$ and $X_{\eta }$ are uniformly homeomorphic for every $0 < \theta , \eta < 1$. We show that this is a rather general phenomenon of the interpolation methods described by the discrete framework of interpolation of Lindemulder and Lorist [A discrete framework for the interpolation of Banach spaces, https://arxiv.org/abs/2105.08373, 2021].References
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Bibliographic Information
- Willian Corrêa
- Affiliation: Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, 13566-590 São Carlos, SP, Brazil
- ORCID: 0000-0003-2172-4019
- Email: willhans@icmc.usp.br
- Received by editor(s): November 28, 2022
- Received by editor(s) in revised form: October 17, 2023, November 6, 2023, November 7, 2023, and November 8, 2023
- Published electronically: March 20, 2024
- Additional Notes: The author was supported by São Paulo Research Foundation (FAPESP), grants 2016/25574-8 and 2021/13401-0.
- Communicated by: Stephen Dilworth
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 2157-2167
- MSC (2020): Primary 46B70, 46B80
- DOI: https://doi.org/10.1090/proc/16730
- MathSciNet review: 4728480