The isometry degree of a computable copy of ℓp¹

Article type: Research Article

Authors: McNicholl, Timothy H.^{a; *} | Stull, Donald M.^b

Affiliations: [a] Department of Mathematics, Iowa State University, Ames, IA, USA. mcnichol@iastate.edu | [b] Campus scientifique, Laboratoire lorrain de recherche en informatique et ses applications, BP 239, 54506 Vandoeuvre-lés Nancy Cedex, France. donald.stull@inria.fr

Correspondence: [*] Corresponding author. mcnichol@iastate.edu.

Note: [1] An abbreviated version of this paper first appeared in the proceedings of the fourteenth Computability in Europe conference.

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.

Keywords: Computable analysis, functional analysis

DOI: 10.3233/COM-180214

Journal: Computability, vol. 8, no. 2, pp. 179-189, 2019