Campus Units

Mathematics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

2017

Journal or Book Title

Computability

Volume

6

Issue

4

First Page

391

Last Page

408

DOI

10.3233/COM-160065

Abstract

Suppose p is a computable real so that p ≥ 1. It is shown that the halting set can compute a surjective linear isometry between any two computable copies of Rᵖ. It is also shown that this result is optimal in that when p /= 2 there are two computable copies of Rᵖ with the property that any oracle that computes a linear isometry of one onto the other must also compute the halting set. Thus, Rᵖ is ∆⁰-categorical and is computably categorical if and only if p = 2. It is also demonstrated that there is a computably categorical Banach space that is not a Hilbert space. These results hold in both the real and complex case.

Comments

This is a manuscript of an article published as McNicholl, Timothy H. "Computable copies of ℓp." Computability 6, no. 4 (2017): 391-408. The final publication is available at IOS Press through http://dx.doi.org/10.3233/COM-160065. Posted with permission.

Copyright Owner

IOS Press and the authors

Language

en

File Format

application/pdf

Published Version

Share

COinS