Bounds on eigenvalues of the product and the Jordan product of two positive definite operators on a finitedimensional Hilbert space
Abstract
New easy proofs are given of the eigenvalue inequalities obtained by AmirMoez for a product AB of two positive definite (strictly positive) operators A and B on a finitedimensional Hilbert space. As a simple consequence of these inequalities, new bounds are established on the eigenvalues of AB which are much sharper than the ones recently given by Sha Huyun. The results is then used to make an easy deduction of a lower bound to the lowest eigenvalue of the Jordan product of A and B. The bound thus obtained is at least as good as the one obtained by Alikakos and Bates.
 Publication:

Letters in Mathematical Physics
 Pub Date:
 January 1989
 DOI:
 10.1007/BF00420015
 Bibcode:
 1989LMaPh..17...55G
 Keywords:

 49G20