The isometry degree of a computable copy of ℓ p 1

Abstract

When p is a computable real so that $p ⩾ 1$ , we define the isometry degree of a computable presentation of $ℓ^{p}$ to be the least powerful Turing degree d by which it is d-computably isometrically isomorphic to the standard presentation of $ℓ^{p}$ . We show that this degree always exists and that when $p \neq 2$ these degrees are precisely the c.e. degrees.

Keywords

Computable analysis functional analysis

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