Weighted holomorphic spaces with trivial closed range multiplication operators

Authors:
Kinga Cichon and Kristian Seip

Journal:
Proc. Amer. Math. Soc. **131** (2003), 201-207

MSC (2000):
Primary 47B38

DOI:
https://doi.org/10.1090/S0002-9939-02-06530-9

Published electronically:
May 22, 2002

MathSciNet review:
1929039

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Abstract: We deal with the space consisting of those analytic functions on the unit disc such that , with . We determine the critical rate of decay of such that the pointwise multiplication operator , and analytic, has closed range in only in the trivial case that is the product of an invertible function in and a finite Blaschke product.

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Additional Information

**Kinga Cichon**

Affiliation:
Faculty of Mathematics and Computer Science, A. Mickiewicz University, ul. Matejki 48/49, 60-769 Poznań, Poland

Email:
bogalska@amu.edu.pl

**Kristian Seip**

Affiliation:
Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway

Email:
seip@math.ntnu.no

DOI:
https://doi.org/10.1090/S0002-9939-02-06530-9

Keywords:
Weighted Banach space of analytic functions,
pointwise multiplication operator,
closed range

Received by editor(s):
April 17, 2001

Received by editor(s) in revised form:
August 21, 2001

Published electronically:
May 22, 2002

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2002
American Mathematical Society