A Note on the Computable Categoricity of \(\ell ^p\) Spaces
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.
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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