UPPER AND LOWER BOUNDS, AND OPERATOR MONOTONICITY OF AN EXTENSION OF THE PETZ-HASEGAWA FUNCTION

作者：Furuta Takayuki; Ito Masatoshi^*; Yamazaki Takeaki; Yanagida Masahiro

来源：Mathematical Inequalities & Applications, 2018, 21(1): 155-164.

DOI：10.7153/mia-2018-21-13

• Positive definite operator
• operator mean
• operator monotone function
• Petz-Hasegawa theorem

The Petz-Hasegawa function f(p)(x) = p(1- p) (x-1)(2) /(x(p) - 1) (x(1-p) - 1)
for p is an element of[-1,2] is a well-known operator monotone function on x > 0. In this paper, we discuss some properties of the following extension of the Petz-Hasegawa function
f (p) (x) = x(gamma) Pi(n)(i-1) pi x-1/x(pi)-1,
where p = (p1, . . . , pn) by only using an elementary technique. Firstly, we get its upper and lower bounds. Secondly, we obtain a result on operator monotonicity.

• 出版日期2018-1