Strengthening of Clarkson-McCarthy inequalities with several operators

2024/08/14 by Teng Zhang, Zhang, Teng
Mathematics · Computer Science · #Mathematical Inequalities and Applications #Optimization and Variational Analysis #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.2408.07730

Abstract

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≤ i≤ 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.

Related

• From Clarkson-McCarthy inequality to Ball-Carlen-Lieb inequality
• Full characterization of existence of Clarkson-McCarthy type inequalities
• Hardy-Littlewood inequalities for multipolynomials
• Clarkson-McCarthy inequalities with unitary and isometry orbits
• A sharper bound for the Jensen's operator inequality