Boundary representations on co-invariant subspaces of Bergman space
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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 $L_a^2(\mathbb {B}_n)$.References
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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
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 615-622
- MSC (2000): Primary 47L55, 46E22
- DOI: https://doi.org/10.1090/S0002-9939-09-10079-5
- MathSciNet review: 2557178