M. Khosravi
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
[ 1 ] - Improvements of Young inequality using the Kantorovich constant
Some improvements of Young inequality and its reverse for positive numbers with Kantorovich constant $K(t, 2)=frac{(1+t)^2}{4t}$ are given. Using these inequalities some operator inequalities and Hilbert-Schmidt norm versions for matrices are proved. In particular, it is shown that if $a, b$ are positive numbers and $0 leqslant nu leqslant 1,$ then for all integers $ kgeqsl...
[ 2 ] - Some weighted operator geometric mean inequalities
In this paper, using the extended Holder- -McCarthy inequality, several inequalities involving the α-weighted geometric mean (0<α<1) of two positive operators are established. In particular, it is proved that if A,B,X,Y∈B(H) such that A and B are two positive invertible operators, then for all r ≥1, ‖X^* (A⋕_α B)Y‖^r≤‖〖(X〗^* AX)^r ‖^((1-α)/2) ‖〖(Y〗^* AY)^r ‖^((1-α)/2) ‖〖(X〗^* BX)^r ‖^(α/2) ‖〖(Y...
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