Enhanced Young-type inequalities utilizing Kantorovich approach for semidefinite matrices

Abstract

This article introduces new Young-type inequalities, leveraging the Kantorovich constant, by refining the original inequality. In addition, we present a range of norm-based inequalities applicable to positive semidefinite matrices, such as the Hilbert-Schmidt norm and the trace norm. The importance of these results lies in their dual significance: they hold inherent value on their own, and they also extend and build upon numerous established results within the existing literature.

Keywords

• kantorovich constant
• unitarily invariant norms
• young-type inequalities
• matrix inequalities
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