In this article, we refine certain earlier existing bounds for Berezin number of operator matrices. We also prove some new Berezin number inequalities for general n × n operator matrices. Further, we establish several upper bounds for Berezin number and generalized Euclidean Berezin number for off-diagonal operator matrices. Finally, some interesting examples are discussed.

中文翻译：

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算子矩阵的别列津数不等式

在本文中，我们改进了 Berezin 运算符矩阵数的某些早期现有边界。我们还证明了一般 n × n 算子矩阵的一些新的 Berezin 数不等式。此外，我们为非对角算子矩阵建立了 Berezin 数和广义 Euclidean Berezin 数的几个上限。最后，讨论了一些有趣的例子。