Theoretical analysis demonstrates convexity of the q-Berezin range for specific operator classes on the Hardy space, indicating its connection to the classical Berezin range.
This article investigates the geometric structure of the q-Berezin range of operators on the Hardy space, with a particular emphasis on convexity. Convexity results are established for several operator classes, including Toeplitz, weighted shift, and certain composition operators. The study demonstrates the relationship between the q-Berezin range and the classical Berezin range.
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Bhattacharya et al. (2026) studied this question.
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