Journal of Operator Theory

Volume 57, Issue 2, Spring 2007 pp. 229-242.

Differences of composition operators on the Bloch spaces

Authors: Takuya Hosokawa (1) and Shuichi Ohno (2)
Author institution: (1) Kosugi-Jinya-cho 1-10-8 402, Nakahara-ku, Kanagawa, 211-0062, Japan
(2) Nippon Institute of Technology, Miyashiro, Minami-Saitama 345-8501, Japan

Summary: We study the boundedness and the compactness of the differences of two composition operators on the Bloch and the little Bloch spaces. We prove that the weak compactness of the differences on the little Bloch space is equivalent to the compactness. Moreover we will give attention to the topological structure of the space of composition operators on the Bloch space in the operator topology.

Keywords: Composition operators, Bloch spaces

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