Abstract
The well-known arithmetic-geometric mean inequality for singular values, according to Bhatia and Kittaneh, says that if and are compact operators on a complex separable Hilbert space, then Hirzallah has proved that if are compact operators, then We give inequality which is equivalent to and more general than the above inequalities, which states that if are compact operators, then
Highlights
Let B H denote the space of all bounded linear operators on a complex separable Hilbert space H, and let denoted positive by s1 T, operator s2 T T, are T *T 1 2 the as eigenvalues of the s1 T s2 T repeated according to multiplicity
For j 1, 2, we prove that the inequalities (1.1) and (1.3) are equivalent
Our second singular value inequality is equivalent to the inequality (1.4)
Summary
We give inequality which is equivalent to and more general than the above inequalities, which states that if Ai, , Bi ,i 1, 2, , n are compact operators, For j 1, 2, We will give a new inequality which generalizes (1.5), and is equivalent to the inequalities (1.1), (1.2), (1.3), (1.4), (1.5), and (1.6): Let A1, A2 , , An , D K H such that For j 1, 2, We will prove a new inequality which generalizes (1.9), and is equivalent to the inequalities (1.8) and (1.9): If A1, A2 , , An , D K H such that
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