Abstract
This paper generalizes the famous Holder type inequalities for positive real numbers to positive operators on an arbitrary complex Hilbert space. We use appropriate integral representations of certain operator-monotone functions to deduce the concavity and convexity of certain maps involving Tracy-Singh products of operators. These results lead to Holder type inequalities for operators concerning Tracy-Singh products, Khatri-Rao products, Tracy-Singh sums, and Khatri-Rao sums. In particular, we obtain Cauchy-Schwarz type inequalities for operators involving Tracy-Singh products and Khatri-Rao products.
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