Non-commutative Callebaut inequality
M. S. Moslehian, J. S. Matharu, J. S. Aujla
TL;DR
This paper develops an operator version of the Callebaut inequality, extending it to matrix forms and involving the Hadamard product, with applications to weighted operator geometric means.
Contribution
It introduces a novel operator and matrix version of the Callebaut inequality, including the Hadamard product, expanding its applicability in matrix analysis.
Findings
Established an operator version of the Callebaut inequality.
Derived a matrix version involving the Hadamard product.
Applied results to weighted operator geometric means.
Abstract
We present an operator version of the Callebaut inequality involving the interpolation paths and apply it to the weighted operator geometric means. We also establish a matrix version of the Callebaut inequality and as a consequence obtain an inequality including the Hadamard product of matrices.
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