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arXiv:2404.14947v1 Announce Type: new
Abstract: Let $\varphi_j$, $j=1,2, \dots, N$, be holomorphic self-maps of the unit disk $\mathbb{D}$ of $\mathbb{C}$. We prove that the compactness of a linear combination of the composition operators $C_{\varphi_j}: f\mapsto f\circ\varphi_j$ on the Hardy space $H^p(\mathbb{D})$ does not depend on $p$ for $0
<\infty$. This answers a conjecture of Choe et al. about the compact differences $C_{\varphi_1} - C_{\varphi_2}$ on $H^p(\mathbb{D})$, $0
<\infty$.
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