Bounds on eigenvalues of the product and the Jordan product of two positive definite operators on a finite-dimensional Hilbert space

✍ Scribed by A. Grubb; C. S. Sharma

• Publisher: Springer
• Year: 1989
• Tongue: English
• Weight: 208 KB
• Volume: 17
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00420015

✦ Synopsis

New easy proofs are given of the eigenvalue inequalities obtained by Amir-Moez for a product AB of two positive definite (strictly positive) operators A and B on a finite-dimensional 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 Hu-yun. The result 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.