Annals of Functional Analysis

Kwong matrices and operator monotone functions on $(0,1)$

Juri Morishita, Takashi Sano, and Shintaro Tachibana

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In this paper we study positive operator monotone functions on $(0, 1)$ which have some differences from those on $(0, \infty):$ we show that for a concave operator monotone function $f$ on $(0, 1),$ the Kwong matrices $K_f(s_1, \dots, s_n)$ are positive semidefinite for all $n$ and $s_i \in (0, 1),$ and $f(s^p)^{1/p}$ for $p \in (0,1]$ and $s/f(s)$ are operator monotone. We also give a sufficient condition for the Kwong matrices to be positive semidefinite.

Article information

Ann. Funct. Anal., Volume 5, Number 1 (2014), 121-127.

First available in Project Euclid: 5 February 2014

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Zentralblatt MATH identifier

Primary: 47A63: Operator inequalities
Secondary: 15B48: Positive matrices and their generalizations; cones of matrices

Kwong matrix operator monotone function Loewner matrix positive semidefinite


Morishita, Juri; Sano, Takashi; Tachibana, Shintaro. Kwong matrices and operator monotone functions on $(0,1)$. Ann. Funct. Anal. 5 (2014), no. 1, 121--127. doi:10.15352/afa/1391614576.

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