A difference of two composition operators on an analytic banach space

Yôsuke Hishikawa; Takahiko Nakazi; Masahiro Yamada

doi:nihmj/1643386843

Abstract

A finite rank difference of two composition operators is studied on an analytic Banach space $\mathcal{B}$ on a domain $\mathcal{D}$ of the complex plane. It is shown that the rank is either zero or one when $\mathcal{D}$ is a bounded domain and $\mathcal{B}$ contains all bounded analytic functions on $\mathcal{D}$ .

Funding Statement

This work is based on research 16K05198 supported by Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science.

Acknowledgments

The authors wish to thank the referee for specific suggestions on earlier version of this paper.

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Yôsuke Hishikawa. Takahiko Nakazi. Masahiro Yamada. "A difference of two composition operators on an analytic banach space." Nihonkai Math. J. 32 (2) 107 - 110, 2021.

Information

Received: 12 November 2020; Revised: 24 September 2021; Published: 2021

First available in Project Euclid: 3 May 2022

Subjects:

Primary: 47B33

Secondary: 47B38

Keywords: Analytic function , Banach space , Composition operator

Abstract

Funding Statement

Acknowledgments

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