Inequalities for the powers of nonnegative Hermitian operators
Inequalities for the powers of nonnegative Hermitian operators
In the set of bounded Hermitian operators from a Hilbert space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H"> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding="application/x-tex">H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> into itself, we define three types of ordering by means of the cones of nonnegative, positive definite and positive invertible operators respectively. Our main theorem shows …