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- W4256669673 abstract "This paper studies the largest ${C^*}$-subalgebra $Q$ of ${L^infty }({mathbf {D}})$ such that the Toeplitz operators ${T_f}$ on the Bergman space $L_a^2({mathbf {D}})$ with symbols $f$ in $Q$ have a symbol calculus modulo the compact operators. $Q$ is characterized by a condition of vanishing mean oscillation near the boundary. I also give several other necessary and sufficient conditions for a bounded function to be in $Q$. After decomposing $Q$ in a nice way, I study the Fredholm theory of Toeplitz operators with symbols in $Q$. The essential spectrum of ${T_f}(f in Q)$ is shown to be connected and computable in terms of the Stone-CÄch compactification of ${mathbf {D}}$. The results in this article partially answer a question posed in [3] and give several new necessary and sufficient conditions for a bounded analytic function on the open unit disc to be in the little Bloch space ${mathcal {B}_0}$." @default.
- W4256669673 created "2022-05-12" @default.
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- W4256669673 date "1987-08-01" @default.
- W4256669673 modified "2023-09-30" @default.
- W4256669673 title "VMO, ESV, and Toeplitz Operators on the Bergman Space" @default.
- W4256669673 doi "https://doi.org/10.2307/2000860" @default.
- W4256669673 hasPublicationYear "1987" @default.
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