JUCS - Journal of Universal Computer Science 19(6): 750-770, doi: 10.3217/jucs-019-06-0750

The Riesz Representation Operator on the Dual of C[0; 1] is Computable

‡ University of Tarbiat Modares, Tehran, Iran

Corresponding author: Tahereh Jafarikhah ( t.jafarikhah@modares.ac.ir ) © Tahereh Jafarikhah, Klaus Weihrauch. This article is freely available under the J.UCS Open Content License. Citation:
Jafarikhah T, Weihrauch K (2013) The Riesz Representation Operator on the Dual of C[0; 1] is Computable. JUCS - Journal of Universal Computer Science 19(6): 750-770. https://doi.org/10.3217/jucs-019-06-0750 |

Abstract

By the Riesz representation theorem, for every linear functional F : C[0; 1] → ℝ there is a function g : [0; 1] → ℝ of bounded variation such that A computable version is proved in [Lu and Weihrauch(2007)]: a function g can be computed from F and its norm, and F can be computed from g and an upper bound of its total variation. In this article we present a much more transparent proof. We first give a new proof of the classical theorem from which we then can derive the computable version easily. As in [Lu and Weihrauch(2007)] we use the framework of TTE, the representation approach for computable analysis, which allows to define natural concepts of computability for the operators under consideration.

Keywords

computable analysis, Riesz representation theorem