On Drury's solution of Bhatia & Kittaneh's question

2016/01/21 by Lin, Minghua
#15A45 #15A60 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1601.05525

Abstract

Let A, B be n× n positive semidefinite matrices. Bhatia and Kittaneh asked whether it is true √(σ_j(AB))≤ (1)/(2) λ_j(A+B), j=1, …, n where σ_j(⋅), λ_j(⋅), are the j-th largest singular value, eigenvalue, respectively. The question was recently solved by Drury in the affirmative. This article revisits Drury's solution. In particular, we simplify the proof for a key auxiliary result in his solution.

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