Differences of weighted composition operators acting from Bloch space to 𝐻^{∞}

Hosokawa, Takuya; Ohno, Shûichi

doi:10.1090/S0002-9947-2011-05245-1

Differences of weighted composition operators acting from Bloch space to $H^\infty$
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by Takuya Hosokawa and Shûichi Ohno

Trans. Amer. Math. Soc. 363 (2011), 5321-5340

DOI: https://doi.org/10.1090/S0002-9947-2011-05245-1

Published electronically: May 5, 2011

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Abstract:

We study the boundedness and compactness of the differences of two weighted composition operators acting from the Bloch space $\mathcal B$ to the space $H^\infty$ of bounded analytic functions on the open unit disk. Such a study has a relationship to the topological structure problem of composition operators on $H^\infty$. Using this relation, we will estimate the operator norms and the essential norms of the differences of two composition operators acting from $\mathcal B$ to $H^\infty$.

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