The Ces\`aro Operator is in the Toeplitz Algebra

Yuanqi Sang

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arXiv · 2608.25740

The Ces\`aro Operator is in the Toeplitz Algebra

Yuanqi Sang

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Abstract

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

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Yuanqi Sang. 2026-08-26. The Ces\`aro Operator is in the Toeplitz Algebra. https://arxiv.org/abs/2608.25740

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