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- W2783619626 abstract "The well-known Axler-Zheng theorem characterizes compactness of finite sums of finite products of Toeplitz operators on the unit disk in terms of the Berezin transform of these operators. Subsequently this theorem was generalized to other domains and appeared in different forms, including domains in $mathbb{C}^n$ on which the $overline{partial}$-Neumann operator $N$ is compact. In this work we remove the assumption on $N$, and we study weighted Bergman spaces on smooth bounded pseudoconvex domains. We prove a local version of the Axler-Zheng theorem characterizing compactness of Toeplitz operators in the algebra generated by symbols continuous up to the boundary in terms of the behavior of the Berezin transform at strongly pseudoconvex points. We employ a Forelli-Rudin type inflation method to handle the weights." @default.
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- W2783619626 date "2018-01-05" @default.
- W2783619626 modified "2023-10-16" @default.
- W2783619626 title "A local weighted Axler–Zheng theorem in ℂn" @default.
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- W2783619626 doi "https://doi.org/10.2140/pjm.2018.294.89" @default.
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