Bellman′s Inequality (II)

Abstract:

      This article concerns a conjecture:ｔｒ（ＡＢ）^ｍ≤ｔｒ（Ａ^ｍＢ^ｍ）which was put forward by Bellman R . We prove it under the additional condition that A∈S_k and B∈I_k. We also investigate the case when A,B are nonnegative.