Ela Inequalities Involving Eigenvalues for Difference of Operator Means∗

In a recent paper by Hirzallah et al. [O. Hirzallah, F. Kittaneh, M. Krnić, N. Lovričević, and J. Pečarić. Eigenvalue inequalities for differences of means of Hilbert space operators. Linear Algebra and its Applications, 436:1516–1527, 2012.], several eigenvalue inequalities are obtained for the difference of weighted arithmetic and weighted geometric means of two positive invertible operators A and B on a separable Hilbert space under the condition that A− B is compact. This paper aims to prove some general versions of eigenvalue inequalities for the difference of weighted arithmetic, weighted geometric and generalized Heinz means with better bounds under the same conditions.