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

 

Boundary representations on co-invariant subspaces of Bergman space


Author: Wei He
Journal: Proc. Amer. Math. Soc. 138 (2010), 615-622
MSC (2000): Primary 47L55, 46E22
Published electronically: September 9, 2009
MathSciNet review: 2557178
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Abstract: Let $ M$ be an invariant subspace of the Bergman space $ L_a^2(\mathbb{D})$ and $ S_M$ be the compression of the coordinate multiplication operator $ M_z$ to the co-invariant subspace $ L_a^2(\mathbb{D})\ominus M$. The present paper determines when the identity representation of $ C^*(S_M)$ is a boundary representation for the Banach subalgebra $ \mathcal{B}(S_M)$. The paper also considers boundary representations on the co-invariant subspaces of $ L_a^2(\mathbb{B}_n)$.


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Additional Information

Wei He
Affiliation: Department of Mathematics, Southeast University, Nanjing, 210018, People’s Republic of China
Email: 051018010@fudan.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10079-5
PII: S 0002-9939(09)10079-5
Received by editor(s): March 28, 2008
Received by editor(s) in revised form: April 20, 2009
Published electronically: September 9, 2009
Communicated by: Marius Junge
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.