考希-施瓦茨不等式的完善与算子数值半径型不等式的完善和概括

Vuk Stojiljković, S. Dragomir
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引用次数: 0

摘要

受先前报告结果的启发,目前的工作旨在通过对著名的考奇-施瓦茨不等式进行新的改进,开发新的希尔伯特空间操作数数值半径上界。特别是,我们给出了一个新的定理 (3.1),并利用它进一步概括了几个向量和数值半径类型的不等式,以及之前给出的 Cauchy-Schwartz 不等式的扩展。具体地说,(2.5) (2.8) (1.6) 已被 (4.3) (4.1) (4.2) 所概括
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Refinement of the Cauchy-Schwartz inequality with refinements and generalizations of the numerical radius type inequalities for operators
Motivated by the results previously reported, the current work aims at developing new numerical radius upper bounds of Hilbert space opera- tors by offering new improvements to the well-known Cauchy-Schwarz inequal- ity. In particular, a novel Lemma (3.1) is given, which is utilized to further generalize several vector and numerical radius type inequalities, as well as pre- viously given extensions of the Cauchy-Schwartz inequality. Specifically, (2.5) (2.8) (1.6) have been generalized by (4.3) (4.1) (4.2)
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