Study on operator theory and operator means

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Operator means can be constructed from certain scalar means in a natural fashion, and comparison of unitarily invariant norms of such operator means requires positive definiteness of ratios of corresponding scalar means. Positive definiteness for many such ratios was determined, and consequently many very precise norm inequalities (such as an abundance of generalizations of the Heinz inequality and monotonicity in a parameter of norms of operator binomial means) were obtained. Moreover, many such positive definite functions arising in this way were shown to be infinitely divisible. Also, Jensen-type majorization results and the equality condition for the trace Jensen inequality were proved in the setting of von Neumann algebras.