A local weighted Axler-Zheng theorem in C-n

Cuckovic, Zeljko and Şahutoğlu, Sönmez and Zeytuncu, Yunus E. (2018) A local weighted Axler-Zheng theorem in C-n. Pacific Journal of Mathematics, 294 (1). pp. 89-106. ISSN 0030-8730

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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 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.
Item Type: Article
Uncontrolled Keywords: Axler-Zheng theorem; Toeplitz operators; pseudoconvex domains
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Sönmez Şahutoğlu
Date Deposited: 13 Feb 2018 16:09
Last Modified: 23 May 2023 12:47
URI: https://research.sabanciuniv.edu/id/eprint/34233

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