| Popis: |
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 $\mathcal{Q}$.
15 pages.To appear in Linear Algebra and Its Applications |
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