Boundary representations on co-invariant subspaces of Bergman space

He, Wei

doi:10.1090/S0002-9939-09-10079-5

Boundary representations on co-invariant subspaces of Bergman space
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Proc. Amer. Math. Soc. 138 (2010), 615-622 Request permission

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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