TY - JOUR
T1 - Comments on conjectures of trace inequalities on a generalized Wigner-Yanase skew information
AU - Ko, Chul Ki
PY - 2010/9
Y1 - 2010/9
N2 - 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.
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.
KW - Trace inequality
KW - Uncertainty relation
KW - Wigner-Yanase skew information
KW - Wigner-Yanase-Dyson skew information
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U2 - 10.1016/j.jmaa.2010.02.037
DO - 10.1016/j.jmaa.2010.02.037
M3 - Article
AN - SCOPUS:77952584701
SN - 0022-247X
VL - 369
SP - 164
EP - 167
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -