Annals of Functional Analysis

Matrix inequalities for the difference between arithmetic mean and harmonic mean

Wenshi Liao and Junliang Wu

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Motivated by the refinements and reverses of arithmetic-geometric mean and arithmetic-harmonic mean inequalities for scalars and matrices, in this article, we generalize the scalar and matrix inequalities for the difference between arithmetic mean and harmonic mean. In addition, relevant inequalities for the Hilbert-Schmidt norm and determinant are established.

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Ann. Funct. Anal., Volume 6, Number 3 (2015), 191-202.

First available in Project Euclid: 17 April 2015

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Zentralblatt MATH identifier

Primary: 15A45: Miscellaneous inequalities involving matrices
Secondary: 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05] 26E60: Means [See also 47A64] 47A63: Operator inequalities

Arithmetic mean harmonic mean matrix inequality positive definite matrix


Liao, Wenshi; Wu, Junliang. Matrix inequalities for the difference between arithmetic mean and harmonic mean. Ann. Funct. Anal. 6 (2015), no. 3, 191--202. doi:10.15352/afa/06-3-16.

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