论文标题
通用数值半径的不平等
Inequalities for the generalized numerical radius
论文作者
论文摘要
在本文中，我们为A. abu-Omar和F. kittaneh在[3]中引入的概述矩阵的广义数值半径提供了几种不等式。我们将M. sababheh在[12]中获得的凸度和对数 - 跨性别的结果概括为数值半径的情况。我们通过为[12]中针对某个矩阵操作员函数的凸的问题提供积极答案来说明我们的工作。此外，在[2]的A. aldalabih和F. kittaneh的结果中，对于Hilbert-Schmidt Numerical Radius Norm，我们使用一些Schatten $ p $ - norm不平等现象，用于分区$ 2 \ times $ 2 \ times 2 $ 2 $ block-block-matrices，以提供几个schatten $ p $ p $ p $ - norm-norm duius rudius radius imerequalies。
In the present paper, we provide several inequalities for the generalized numerical radius of operator matrices as introduced by A. Abu-omar and F. Kittaneh in [3]. We generalize the convexity and the log-convexity results obtained by M. Sababheh in [12] for the case of the numerical radius to the case of the generalized numerical radius. We illustrate our work by providing a positive answer for the question addressed in [12] for the convexity of a certain matrix operator function. Moreover, and motivated by the results of A. Aldalabih and F. Kittaneh in [2] for the case of Hilbert-Schmidt numerical radius norm, we use some Schatten $p$-norm inequalities for partitioned $2\times 2$ block-matrices to provide several Schatten $p$-norm numerical radius inequalities.
