正交投影线性组合的不等式及其应用

IF 0.9 3区 数学 Q2 MATHEMATICS
Najla Altwaijry, Cristian Conde, Silvestru Sever Dragomir, Kais Feki
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引用次数: 0

摘要

在本文中,我们提出了有关正交投影线性组合的各种不等式。这些结果旨在概括和完善众所周知的不等式,例如布扎诺和奥斯特洛夫斯基提出的不等式。此外,我们还研究了这些线性组合的一种特殊情况,并引入了对考希-施瓦茨不等式的新改进。此外,我们还得出了一些与有界线性算子的协方差和方差有关的结论。此外,作为我们一些结果的应用,我们建立了几个涉及三个算子乘积的不等式,其中一个是正交投影和同一算子的线性组合。最后,我们用正交投影和同一算子引入了一个新的正算子结构,并推导出了涉及它的一些规范和数值半径不等式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Inequalities for linear combinations of orthogonal projections and applications

In this paper, we present various inequalities regarding the linear combinations of orthogonal projections. These results aim to generalize and refine well-known inequalities, such as those due to Buzano and Ostrowski. Additionally, we investigate a specific case of these linear combinations and introduce new refinements of the Cauchy–Schwarz inequality. Furthermore, we establish some findings related to the covariance and variance of bounded linear operators. Moreover, as applications of some of our results, we establish several inequalities involving the product of three operators, one of which is a linear combination of an orthogonal projection and the identity operator. Finally, we introduce a new positive operator construction in terms of an orthogonal projection and the identity operator, and we derive some norms and numerical radius inequalities involving it.

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来源期刊
CiteScore
2.20
自引率
9.10%
发文量
59
期刊介绍: The Journal of Pseudo-Differential Operators and Applications is a forum for high quality papers in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.
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