q-贝雷津扇形算子及其在q-贝雷津数不等式和q-贝雷津值域中的应用
$q$-Berezin sectorial operators with applications to $q$-Berezin number inequalities and $q$-Berezin ranges
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中文总结 AI 辅助
本文引入q-贝雷津扇形算子，证明其为q-扇形算子的推广，推导其q-贝雷津数的新不等式，并研究Bergman空间上算子的q-贝雷津值域几何结构。
中文摘要 AI 辅助
本文引入一类新的算子，称为q-贝雷津扇形算子，作为q-扇形算子类的推广。通过在Hardy-Hilbert空间上给出的例子，证明存在算子是q-贝雷津扇形算子但非q-扇形算子。还推导了这类算子对应的q-贝雷津数的若干新不等式。此外，研究了Bergman空间上各类算子的q-贝雷津值域的几何结构，包括加权移位算子和特定复合算子。
英文摘要
In this paper, we introduce a new class of operators, called $q$-Berezin sectorial operators, as an extension of the class of $q$-sectorial operators. By presenting examples on the Hardy-Hilbert space, we show that there exist operators which are $q$-Berezin sectorial but not $q$-sectorial. Several new inequalities for the $q$-Berezin number associated with this class of operators are also derived. In addition, we investigate the geometric structure of the $q$-Berezin range for various classes of operators on the Bergman space, including weighted shift and certain composition operators.
