Abstract
Suppose that \(p\) is a computable real and that \(p \ge 1\). We show that in both the real and complex case, \(\ell ^p\) is computably categorical if and only if \(p = 2\). The proof uses Lamperti’s characterization of the isometries of Lebesgue spaces of \(\sigma \)-finite measure spaces.
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Acknowledgement
The author thanks the anonymous referees who made helpful comments. The author’s participation in CiE 2015 was funded by a Simons Foundation Collaboration Grant for Mathematicians.
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McNicholl, T.H. (2015). A Note on the Computable Categoricity of \(\ell ^p\) Spaces. In: Beckmann, A., Mitrana, V., Soskova, M. (eds) Evolving Computability. CiE 2015. Lecture Notes in Computer Science(), vol 9136. Springer, Cham. https://doi.org/10.1007/978-3-319-20028-6_27
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DOI: https://doi.org/10.1007/978-3-319-20028-6_27
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