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Transactions of the American Mathematical Society

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Differences of weighted composition operators acting from Bloch space to $ H^\infty$


Authors: Takuya Hosokawa and Shûichi Ohno
Journal: Trans. Amer. Math. Soc. 363 (2011), 5321-5340
MSC (2010): Primary 47B33
DOI: https://doi.org/10.1090/S0002-9947-2011-05245-1
Published electronically: May 5, 2011
MathSciNet review: 2813417
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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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Additional Information

Takuya Hosokawa
Affiliation: Faculty of Engineering, Ibaraki University, Hitachi, Ibaraki, 316-8511, Japan
Email: hoso-t@mx.ibaraki.ac.jp

Shûichi Ohno
Affiliation: Nippon Institute of Technology, Miyashiro, Minami-Saitama 345-8501, Japan
Email: ohno@nit.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-2011-05245-1
Keywords: Composition operators, the space of bounded analytic functions, Bloch spaces.
Received by editor(s): July 9, 2008
Received by editor(s) in revised form: October 2, 2009
Published electronically: May 5, 2011
Additional Notes: The first author was partially supported by the Korean Research Foundation Grant funded by the Korean Government (KRF-2008-314-C00012).
The second author was partially supported by Grant-in-Aid for Scientific Research (No.20540185), Japan Society for the Promotion of Science.
Article copyright: © Copyright 2011 American Mathematical Society