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

By Jean-Christophe Bourin, Mitsuru Uchiyama. 2007

95 citations recorded by the source corpus.

Abstract 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,∞), ‖ f ( A + B ) ‖ ⩽ ‖ f ( A ) + f ( B ) ‖ 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 ∗ X B ∞ ⩽ max X | ‖ ∞ ; ‖ | B | + | X ∗ | ‖ ∞ } for any partitioned Hermitian matrix.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8ff50cd6dfd188e0c1044270561fc101483be0f5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Fumio Hiai
2. Jean-Christophe Bourin
3. P. Denes

In Geometry and Topology

1. Fumio Hiai
2. P. Denes

Citations in the corpus

• Unitary orbits of Hermitian operators with convex or concave functions (2011, background): “The case of operator concave functions is given in [2] and the general case is established in [14]; see also [12] for further results.”
• Introduction to Matrix Analysis and Applications (2014, background): “31 was proved by Bourin and Uchiyama [28], which is the second main result.”