Path connected components in weighted composition operators on and 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

MathSciNet review:
3042596

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

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