若干算子的 Clarkson-McCarthy 不等式的加强
Strengthening of Clarkson-McCarthy inequalities with several operators
AI总结：
本文通过扩展 Bourin-Lee 方法，建立并推广了涉及若干算子的加强型 Clarkson-McCarthy 不等式，证实既有猜想并改进相关结果。
摘要：
本文建立了两个涉及若干算子的 Clarkson-McCarthy 不等式的加强形式。这些结果不仅证实了作者在 [Israel J. Math. 2024] 中提出的一个猜想，还改进了 Hirazallah-Kittaneh 在 [Integral Equations Operator Theory 60 (2008)] 以及 Bhatia-Kittaneh 在 [Bull. London Math. Soc. 36 (2004)] 中的结果。我们还将一个结果推广到算子对 $(A_i,B_i), 1\le i\le n$，并得到另一个不等式的另一种形式。文中也讨论了这些不等式的无限情形。该方法是对 Bourin 和 Lee 在 [Linear Algebra Appl. 601 (2020)] 中所得结果的扩展。此外，还得到了一些相关的特征值不等式。
英文摘要：
Strengthening of two Clarkson-McCarthy inequalities with several operators is established. These not only confirm a conjecture of the author in [Israel J. Math. 2024], but also improve results of Hirazallah-Kittaneh in [Integral Equations Operator Theory 60 (2008)] and Bhatia-Kittaneh in [Bull. London Math. Soc. 36 (2004)]. We also give a generalization of a result for pairs $(A_i,B_i), 1\le i\le n$ and obtain another form of another inequality. The infinite cases of these inequalities are also discussed. The method is an extension of the result obtained by Bourin and Lee in [Linear Algebra Appl. 601 (2020)]. Some related eigenvalue inequalities are also obtained.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
