Choi–Davis–Jensen’s type trace inequalities for convex functions of self-adjoint operators in Hilbert spaces

Abstract

Some Choi–Davis–Jensen’s type trace inequalities for convex functions are proved. Also, we generalize these inequalities for any arbitrary operator mean via operator monotone decreasing functions. In particular, we present some new order among \(\mathrm{tr}(\Phi (C)A)\) and \(\mathrm{tr}(\Phi (C)A^{-1})\). New refinements of some power type trace inequalities via reverse and refinement of Young’s inequality are established. Among our results, we obtain new versions of the Hölder type trace inequality for any arbitrary operator mean.

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Correspondence to Silvestru Sever Dragomir.

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Jafarmanesh, H., Shateri, T.L. & Dragomir, S.S. Choi–Davis–Jensen’s type trace inequalities for convex functions of self-adjoint operators in Hilbert spaces. Bol. Soc. Mat. Mex. 26, 1195–1215 (2020). https://doi.org/10.1007/s40590-020-00300-4

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Keywords

  • Choi–Davis–Jensen’s inequality
  • Hölder operator inequality
  • Trace
  • Operator mean
  • Positive linear maps

Mathematics Subject Classification

  • Primary 47A63
  • Secondary 47A99