The Cesàro Operator is in the Toeplitz Algebra

Abstract

Let $\mathbf{T}$ denote the $C^{\ast }$-algebra generated by all bounded Toeplitz operators on the Hardy space of the unit disk. Barr\'ıa and Halmos [\emph{Trans. Amer. Math. Soc.} \textbf{273} (1982), no.~2, 621--630] asked whether the Cesàro operator belongs to $\mathbf{T}$. We answer this question affirmatively.