The Toeplitz algebra has nuclear dimension one

TL;DR

This paper proves that the Toeplitz algebra has nuclear dimension one by constructing specific approximations and utilizing advanced operator algebra techniques.

Contribution

It introduces a novel construction of 2-colourable completely positive approximations for the Toeplitz algebra, establishing its nuclear dimension.

Findings

Nuclear dimension of the Toeplitz algebra is one.

Constructed 2-colourable completely positive approximations.

Utilized projectivity and Lin's theorem in the proof.

Abstract

We prove the title by constructing 2-colourable completely positive approximations for the Toeplitz algebra. Besides results about nuclear dimension and completely positive contractive order zero maps, our argument involves projectivity of the cone over a finite dimensional C*-algebra and Lin's theorem on almost normal matrices.