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arXiv · 2101.03585

Idempotent, model, and Toeplitz operators attaining their norms

Neeru Bala·Kousik Dhara·Jaydeb Sarkar·Aryaman Sensarma
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Abstract

We study idempotent, model, and Toeplitz operators that attain the norm. Notably, we prove that if $\mathcal{Q}$ is a backward shift invariant subspace of the Hardy space $H^2(\mathbb{D})$, then the model operator $S_{\mathcal{Q}}$ attains its norm. Here $S_{\mathcal{Q}} = P_{\mathcal{Q}}M_z|_{\mathcal{Q}}$, the compression of the shift $M_z$ on the Hardy space $H^2(\mathbb{D})$ to $\mathcal{Q}$.

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Neeru Bala, Kousik Dhara, Jaydeb Sarkar, Aryaman Sensarma. 2021-01-10. Idempotent, model, and Toeplitz operators attaining their norms. https://arxiv.org/abs/2101.03585

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