A Note on the Computable Categoricity of l(p) Spaces

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2015-01-01
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Suppose that p is a computable real and that p >= 1. We show that in both the real and complex case, l(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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This is a manuscript of a proceeding published as McNicholl, T., A Note on the Computable Categoricity of l(p) Spaces, Evolving Computability, Proceedings of the 11th Conference on Computability in Europe, Lecture Notes in Computer Science, 9136 (2015): 268, doi: 10.1007/978-3-319-20028-6_27. Posted with permission. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-20028-6_27.

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Thu Jan 01 00:00:00 UTC 2015