A norm inequality for pairs of commuting positive semidefinite matrices

2014/11/23 by Koenraad M. R. Audenaert, Audenaert, Koenraad M. R.
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1411.6234

4 pages

arxiv created 2014/11/23 · arxiv updated 2014/11/25

Abstract

For k=1,…,K, let A_k and B_k be positive semidefinite matrices such that, for each k, A_k commutes with B_k. We show that, for any unitarily invariant norm, |||∑_k=1^K A_kB_k||| ≤ ||| (∑_k=1^K A_k) (∑_k=1^K B_k)|||.

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