A Matrix Trace Inequality for Products of Hermitian Matrices

In this note, the following matrix trace inequality for products of Hermitian matrices A and B, tr AB.2 kFtr A2kB2k., is established, where k is an integer. The above inequality also partly answers a conjecture in Bellman win ‘‘Proceedings of the 2nd International Conference on General Inequalities’’ E. F. Beckenbach, Ed.., pp. 89]90, Birkh¨auser, Basel, 1980x.