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Norm inequalities related to the matrix geometric mean. (English) Zbl 1252.15023

For pairs of positive definite matrices \(A\) and \(B\) this paper proves norm comparisons between several of their matrix means and their \(t\)-generalizations. The proofs rely on showing monotonicity of certain means function of their ordered eigenvalues.

MSC:

15A45 Miscellaneous inequalities involving matrices
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
15A42 Inequalities involving eigenvalues and eigenvectors
47A30 Norms (inequalities, more than one norm, etc.) of linear operators
47A64 Operator means involving linear operators, shorted linear operators, etc.
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