Abstract. We improve and generalize some operator inequalities for positive linear maps. It is shown, among other inequalities, that if 0andWe also obtain an improvement of operator Pólya-Szegö inequality.
We show the following result: Let A be a positive operator satisfying 0 < m1 H ≤ A ≤ M 1 H for some scalars m, M with m < M and Φ be a normalized positive linear map, thenBesides, we prove that the second inequality in the above can be squared.
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