In this paper, we offer an effective method for deducing a number of already known as well as new trace characterizations. Those characterizations are related to inequalities concerning various versions of the geometric mean or different notions of relative entropy. Besides, our method provides new characterizations of the centrality of elements and the commutativity of 𝐶 ∗ -algebras.
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Han et al. (2026) studied this question.
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