A matrix subadditivity inequality for f(A + B) and f(A) + f(B)

✍ Scribed by Jean-Christophe Bourin; Mitsuru Uchiyama

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 120 KB
• Volume: 423
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2007.02.019

✦ Synopsis

In 1999 Ando and Zhan proved a subadditivity inequality for operator concave functions. We extend it to all concave functions: Given positive semidefinite matrices A, B and a non-negative concave function f on [0, ∞),

for all symmetric norms (in particular for all Schatten p-norms). The case f (t) = √ t is connected to some block-matrix inequalities, for instance the operator norm inequality A X *