Let φ be a positive linear functional on Mn (C) and f, g mutually conjugate in the sense of Young. In this note we show a necessary and sufficient condition for the inequality| φ (A* B) | ≦ φ fenced(f (| A |)) + φ fenced(g (| B |)) (A, B ∈ Mn (C))in terms of φ and f. We also see that the inequalityφ (| A* B |) ≦ φ (f (| A |)) + φ (g (| B |)) (A, B ∈ Mn (C))implies the trace property of φ. © 2009 Elsevier Inc. All rights reserved.
Cho, K., & Sano, T. (2009). Young’s inequality and trace. Linear Algebra and Its Applications, 431(8), 1218–1222. https://doi.org/10.1016/j.laa.2009.04.016