Comments on conjectures of trace inequalities on a generalized Wigner-Yanase skew information

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Abstract

Furuichi, Yanagi and Kuriyama gave three conjectures of trace inequalities on the Wigner-Yanase-Dyson skew information and a generalized Wigner-Yanase skew information (Furuichi et al. (2009) [1]) and Yanagi found a counterexample showing that two of the three conjectures don't hold (Yanagi (2010) [6]). In this note, we show that the last conjecture does not hold in general. In addition, we show that in the case of 2×2 matrices the conjecture is true.

Original languageEnglish
Pages (from-to)164-167
Number of pages4
JournalJournal of Mathematical Analysis and Applications
Volume369
Issue number1
DOIs
Publication statusPublished - 2010 Sep 1

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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