We introduce a new norm on the space of all bounded linear operators on a complex Hilbert space, which generalizes the numerical radius norm, the usual operator norm and the modified Davis–Wielandt radius norm. We study basic properties of this norm, including the upper and the lower bounds for it. As an application of the present study, we estimate bounds for the numerical radius of bounded linear operators. We illustrate that our results improve on some of the important existing numerical radius inequalities. Other application of this new norm have also studied.

中文翻译：

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关于 $$\mathcal {B}({\mathcal {H}})$$ B ( H ) 的新范数及其在数值半径不等式中的应用

我们在复 Hilbert 空间上的所有有界线性算子的空间上引入了一个新范数，它概括了数值半径范数、常用算子范数和修正的戴维斯-维兰特半径范数。我们研究这个范数的基本属性，包括它的上限和下限。作为本研究的一个应用，我们估计了有界线性算子的数值半径的界限。我们说明我们的结果改进了一些重要的现有数值半径不等式。还研究了这种新规范的其他应用。