Abstract
In this paper, we prove several unitarily invariant norm inequalities for positive semidefinite matrices. Some of these results give generalizations of earlier known inequalities. Among other applications of our inequalities, we obtain the commutator inequality‖XY−YX‖≤‖X‖‖Y‖+12‖X⁎Y−YX⁎‖for all n × n complex matrices X,Y. Here, ‖⋅‖ denotes the spectral norm.
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