Abstract
In this short note, we provide alternative proofs for several recent results due to Audenaert (Oper. Matrices 9:475–479, 2015) and Zou (J. Math. Inequal. 10:1119–1122, 2016; Linear Algebra Appl. 552:154–162, 2019).
Highlights
Let Mn be the set of n × n complex matrices
For A ∈ Mn, the singular values and eigenvalues of A are denoted by σi(A) and λi(A), respectively, i = 1, . . . , n
Albadawi [3] obtained a stronger version of the Hölder inequality for unitarily invariant norms
Summary
Let Mn be the set of n × n complex matrices. For A ∈ Mn, the singular values and eigenvalues of A are denoted by σi(A) and λi(A), respectively, i = 1, . . . , n. Let A, B ∈ Mn. Bhatia and Kittaneh [8] proved an arithmetic–geometric mean inequality for unitarily invariant norms For A, X, B ∈ Mn. Albadawi [3] obtained a stronger version of the Hölder inequality for unitarily invariant norms. Lin [12] gave a new proof of inequality (6).
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