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Glasgow Mathematical Journal Glasgow Mathematical Journal

Article contents

COMPOSITION OPERATORS ON FINITE RANK MODEL SUBSPACES

Published online by Cambridge University Press:  02 August 2012

JAVAD MASHREGHI  and
MAHMOOD SHABANKHAH
JAVAD MASHREGHI
Affiliation:
Département de mathématiques et de statistique, Université Laval, Québec G1K 7P4, Canada e-mail: javad.mashreghi@mat.ulaval.ca
MAHMOOD SHABANKHAH
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, Québec H3A 2K6, Canada e-mail: mshaban@math.mcgill.ca
Corresponding
E-mail address:
javad.mashreghi@mat.ulaval.ca
mshaban@math.mcgill.ca
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Abstract

We give a complete description of bounded composition operators on model subspaces KB, where B is a finite Blaschke product. In particular, if B has at least one finite pole, we show that the collection of all bounded composition operators on KB has a group structure. Moreover, if B has at least two distinct finite poles, this group is finite and cyclic.

Keywords

Primary: 47B33 Secondary: 30D50 32A35
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 1 , January 2013 , pp. 69 - 83
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

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