Young's inequality and trace

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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.

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