Improved reverse arithmetic-geometric means inequalities for positive operators on Hilbert space

Some means inequalities for positive operators in Hilbert spaces

In this paper, we obtain two refinements of the ordering relations among Heinz means with different parameters via the Taylor series of some hyperbolic functions and by the way, we derive new generalizations of Heinz operator inequalities. Moreover, we establish a matrix version of Heinz inequality for the Hilbert-Schmidt norm. Finally, we introduce a weighted multivariate geometric mean and sh...

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

Optimal Inequalities between Harmonic, Geometric, Logarithmic, and Arithmetic-Geometric Means

A Note on the Weighted Harmonic–geometric–arithmetic Means Inequalities

In this note, we derive non trivial sharp bounds related to the weighted harmonicgeometric-arithmetic means inequalities, when two out of the three terms are known. As application, we give an explicit bound for the trace of the inverse of a symmetric positive definite matrix and an inequality related to the coefficients of polynomials with positive roots. Mathematics subject classification (201...

Optimal Inequalities for Generalized Logarithmic, Arithmetic, and Geometric Means

Copyright q 2010 B.-Y. Long and Y.-M. Chu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. For p ∈ R, the generalized logarithmic mean L p a, b, arithmetic mean Aa, b, and geometric mean Ga, b of two positive numbers a and b are d...