Abstract
In this paper, we establish certain refinements and reverses of Callebaut-type inequality for bounded continuous fields of Hilbert space operators, parametrized by a locally compact Hausdorff space equipped with a finite Radon measure. These inequalities involve Tracy-Singh products, Khatri-Rao products and weighted geometric means. In addition, we obtain integral Callebauttype inequalities for tensor products and Hadamard products. Our results extend Callebaut-type inequalities for real numbers, matrices and operators.
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