Singular value and norm inequalities for positive semidefinite matrices

Abstract

We prove several singular value and norm inequalities involving generalized commutators and anticommutators of positive semidefinite matrices. These inequalities improve and extend earlier known inequalities, including an inequality due to Davidson and Power, which is useful in best approximation of C* −algebras.

Keywords:

• Commutator
• anticommutator
• positive semidefinite matrix
• singular value
• unitarily invariant norm
• inequality

2010 Mathematics Subject Classifications:

• Primary 15A60
• Secondary 15A18
• 15A42
• 47A30
• 47B15

Disclosure statement

No potential conflict of interest was reported by the author(s).