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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Path connected components in weighted composition operators on $ h^\infty$ and $ H^\infty$ with the operator norm


Authors: Kei Ji Izuchi, Yuko Izuchi and Shûichi Ohno
Journal: Trans. Amer. Math. Soc. 365 (2013), 3593-3612
MSC (2010): Primary 47B38; Secondary 30H10
Published electronically: December 13, 2012
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Abstract: We consider the component problem on the sets of weighted composition operators on the spaces of bounded harmonic and analytic functions on the open unit disk with the operator norms, respectively. Especially, we shall determine path connected components in the sets of noncompact weighted composition operators.


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Additional Information

Kei Ji Izuchi
Affiliation: Department of Mathematics, Niigata University, Niigata 950-2181, Japan
Email: izuchi@m.sc.niigata-u.ac.jp

Yuko Izuchi
Affiliation: Aoyama-shinmachi 18-6-301, Niigata 950-2006, Japan
Email: yfd10198@nifty.com

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

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05730-8
PII: S 0002-9947(2012)05730-8
Keywords: Weighted composition operator, the space of bounded harmonic functions, the space of bounded analytic functions, essential norm, path connected component.
Received by editor(s): May 3, 2011
Received by editor(s) in revised form: August 22, 2011
Published electronically: December 13, 2012
Additional Notes: The first author was partially supported by Grant-in-Aid for Scientific Research (No. 21540166), Japan Society for the Promotion of Science.
The third author was partially supported by Grant-in-Aid for Scientific Research (No. 20540185), Japan Society for the Promotion of Science.
Article copyright: © Copyright 2012 American Mathematical Society