In this paper we present new upper bounds for the numerical radius of bounded linear operators defined on a complex Hilbert space. Further we obtain estimations for upper bounds for the numerical radius of the sum of the product of bounded linear operators. We show that the bounds obtained here improve on the existing well-known upper bounds.

中文翻译：

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希尔伯特空间算子数值半径的新上限

在本文中，我们为复杂的希尔伯特空间上定义的有界线性算子的数值半径提供了新的上限。此外，我们获得了有界线性算子乘积之和的数值半径上限的估计。我们表明，此处获得的边界在现有的已知上限上有所改善。