Dense quasi-free subalgebras of the Toeplitz algebra

TL;DR

This paper introduces a family of dense subalgebras within the Toeplitz algebra, establishing conditions for quasi-freeness and demonstrating that Cuntz's smooth Toeplitz algebra is quasi-free.

Contribution

It presents new dense subalgebras of the Toeplitz algebra and provides criteria for their quasi-freeness, including a proof for Cuntz's algebra.

Findings

Established conditions for quasi-freeness of the new subalgebras

Proved Cuntz's smooth Toeplitz algebra is quasi-free

Introduced a new family of dense subalgebras

Abstract

We introduce a family of dense subalgebras of the Toeplitz algebra and give conditions under which our algebras are quasi-free. As a corollary, we show that the smooth Toeplitz algebra introduced by Cuntz is quasi-free.