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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)



Complex symmetry of composition operators induced by involutive ball automorphisms

Author: S. Waleed Noor
Journal: Proc. Amer. Math. Soc. 142 (2014), 3103-3107
MSC (2010): Primary 47B33, 47B32, 47B99; Secondary 47B35
Published electronically: May 15, 2014
MathSciNet review: 3223366
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Abstract: Suppose $ \mathcal {H}$ is a weighted Hardy space of analytic functions on the unit ball $ \mathbb{B}_n\subset \mathbb{C}^n$ such that the composition operator $ C_\psi $ defined by $ C_{\psi }f=f\circ \psi $ is bounded on $ \mathcal {H}$ whenever $ \psi $ is a linear fractional self-map of $ \mathbb{B}_n$. If $ \varphi $ is an involutive Moebius automorphism of $ \mathbb{B}_n$, we find a conjugation operator $ \mathcal {J}$ on $ \mathcal {H}$ such that $ C_{\varphi }=\mathcal {J} C^*_{\varphi }\mathcal {J}$. The case $ n=1$ answers a question of Garcia and Hammond.

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Additional Information

S. Waleed Noor
Affiliation: Abdus Salam School of Mathematical Sciences, New Muslim Town, Lahore, Pakistan
Address at time of publication: Departamento de Matemática, ICMC-USP, São Carlos-SP, Brazil
Email: waleed{\textunderscore}

Keywords: Complex symmetric operator, conjugation, Moebius automorphism, composition operator, normal operator
Received by editor(s): August 31, 2012
Received by editor(s) in revised form: September 17, 2012
Published electronically: May 15, 2014
Communicated by: Pamela B. Gorkin
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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