On the Pólya-Szegö operator inequality

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. ************************************************************************************************************************** **************************************************************************************************************************