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Inequalities for the Powers of Nonnegative Hermitian Operators

1975
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Proceedings of the American Mathematical Society
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In the set of bounded Hermitian operators from a Hubert space H 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 that for all three types of ordering, if A is "greater" than B, then Ar is "greater" than Br for all real numbers r s 1. This generalizes the results of Heinz [3] and Kato UJ-Notice that in finite-dimensional spaces, (2) and (3) are equivalent.

doi:10.2307/2040330
fatcat:wxdc7a5jwnarnmwtjhmz2i5sfi