The isometry degree of a computable copy of ℓp

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2019_McNicholl_IsometryDegreeManuscript.pdf (337.55 KB)
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2019-06-17
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McNicholl, Timothy
 Stull, Donald
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Abstract

When p is a computable real so that p⩾1, we define the isometry degree of a computable presentation of ℓp to be the least powerful Turing degree d by which it is d-computably isometrically isomorphic to the standard presentation of ℓp. We show that this degree always exists and that when p≠2 these degrees are precisely the c.e. degrees.
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This is a manuscript of an article published as McNicholl, Timothy H., and Donald M. Stull. "The isometry degree of a computable copy of ℓp." Computability 8, no. 2 (2019): 179-189.The final publication is available at IOS Press through http://dx.doi.org/10.3233/COM-180214. Posted with permssion.
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https://dr.lib.iastate.edu/handle/20.500.12876/96655
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10.3233/COM-180214
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