New log-majorization results concerning eigenvalues and singular values and a complement of a norm inequality
Abstract
The purpose of this paper is to establish new log-majorization results concerning eigenvalues and singular values which generalize some previous work related to a conjecture and an open question which were presented by R. Lemos and G. Soares in lemos. In addition, we present a complement of a unitarily invariant norm inequality which was conjectured by R. Bhatia, Y. Lim and T. Yamazaki in Bhatia2, and recently proved by T.H. Dinh, R. Dumitru and J.A. Franco in Dinh for the Schatten p-norm with 1≤ p≤ ∞.
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