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arXiv · 1605.00641

The isometry degree of a computable copy of $\ell^p$

Timothy H. McNicholl·D. M. Stull
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Abstract

When $p$ is a computable real so that $p \geq 1$, the isometry degree of a computable copy $\mathcal{B}$ of $\ell^p$ is defined to be the least powerful Turing degree that computes a linear isometry of $\ell^p$ onto $\mathcal{B}$. We show that this degree always exists and that when $p \neq 2$ these degrees are precisely the c.e. degrees.

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Timothy H. McNicholl, D. M. Stull. 2016-05-02. The isometry degree of a computable copy of $\ell^p$. https://arxiv.org/abs/1605.00641

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