On the Pólya-Szegö operator inequality

Abstract

In this paper, we present generalized Pólya-Szegö type inequalities for positive invertible operators on a Hilbert space for arbitrary operator means between the arithmetic and the harmonic means. As applications, we present operator Grüss, Diaz–Metcalf, and Klamkin–McLenaghan inequalities.

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Keywords

• Operator inequality
• operator mean
• positive linear map
• Pólya-Szegö inequality
• operator monotone functions

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