The Cesaro Operator in $\ell^{2}$ is Essentially Normal

Uğur Gül

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arXiv · 2311.15245

The Cesaro Operator in $\ell^{2}$ is Essentially Normal

Uğur Gül

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Abstract

In this paper we prove that the Cesaro operator $\mathcal{C}$ in $\ell^{2}$, the Hilbert space of square summable sequences, is essentially normal, i.e. the commutator $[\mathcal{C}^{\ast},\mathcal{C}]:=\mathcal{C}^{\ast}\mathcal{C}-\mathcal{C}\mathcal{C}^{\ast}$ is a compact operator on $\ell^{2}$.

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Uğur Gül. 2023-11-26. The Cesaro Operator in $\ell^{2}$ is Essentially Normal. https://arxiv.org/abs/2311.15245

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