Operators in the Toeplitz Algebra on the Bergman Space

Nina Zorboska ()
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Nina Zorboska: University of Manitoba, Department of Mathematics

Chapter 83 in Operator Theory, 2026, pp 2581-2601 from Springer

Abstract: Abstract We survey some recent results about operators on the Bergman space, related to the following two questions: when does the boundary vanishing of the Berezin transform determine compactness of the operator, and how can one determine if a general operator is in the Toeplitz algebra or not? We present an interesting variety of results that provide some particular answers. Moreover, they also reveal connections between these two questions and, even more generally, display deep connections between mathematical areas such as complex analysis, measure theory, and operator theory.

Keywords: Toeplitz operators; Berezin transform; Carleson measures; Bergman space; Reproducing kernel Hilbert spaces; Primary 47B35; Secondary 30H25, 46E22 (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-16356-1_114

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DOI: 10.1007/978-3-032-16356-1_114

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