TY  - JOUR
AB  - © 2016 The Author(s). We derive new characterizations of the matrix ?-entropy functionals introduced in Chen & Tropp (Chen, Tropp 2014 Electron. J. Prob. 19, 1-30. (doi:10.1214/ejp.v19-2964)). These characterizations help us to better understand the properties of matrix ?-entropies, and are a powerful tool for establishing matrix concentration inequalities for random matrices. Then, we propose an operator-valued generalization of matrix ?-entropy functionals, and prove the subadditivity under Löwner partial ordering. Our results demonstrate that the subadditivity of operator-valued ?-entropies is equivalent to the convexity. As an application, we derive the operator Efron-Stein inequality.
AU  - Cheng, HC
AU  - Hsieh, MH
DA  - 2016/03/01
DO  - 10.1098/rspa.2015.0563
JO  - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
PY  - 2016/03/01
TI  - Characterizations of matrix and operator-valued ?-entropies, and operator Efron-Stein inequalities
VL  - 472
Y1  - 2016/03/01
Y2  - 2026/05/22
ER  -