## A local weighted Axler-Zheng theorem in C-nCuckovic, Zeljko and Şahutoğlu, Sönmez and Zeytuncu, Yunus E. (2018) Full text not available from this repository. Official URL: http://dx.doi.org/10.2140/pjm.2018.294.89 ## AbstractThe 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 C-n on which the (partial derivative) over bar -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.
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