We prove new inequalities for the spectral radius, essential spectral radius, operator norm, measure of noncompactness and numerical radius of Hadamard weighted geometric mean of (infinite or finite) nonnegative matrices that define positive operators on Banach sequence spaces. Some of these inequalities complement the known inequalities and some of them refine known inequalities. Several inequalities appear to be new even in the finite dimensional case.

中文翻译：

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Banach序列空间上正算子的谱半径和基本谱半径的不等式

我们证明了光谱半径，基本光谱半径，算子范数，非紧致性的度量和Hadamard加权平均数（无限或有限）非负矩阵的几何半径的不等式，它们定义了Banach序列空间上的正算子。这些不平等中的一些补充了已知的不平等，另一些则完善了已知的不平等。即使在有限维情况下，几个不等式似乎也是新的。