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

Chul Ki Ko

doi:10.1016/j.jmaa.2010.02.037

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

Chul Ki Ko

University College

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 language	English
Pages (from-to)	164-167
Number of pages	4
Journal	Journal of Mathematical Analysis and Applications
Volume	369
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2010.02.037
Publication status	Published - 2010 Sept

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jmaa.2010.02.037

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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.",

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AB - 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.

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

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