## Annals of Functional Analysis

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

#### Abstract

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

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

Dates
First available in Project Euclid: 5 February 2014

https://projecteuclid.org/euclid.afa/1391614576

Digital Object Identifier
doi:10.15352/afa/1391614576

Mathematical Reviews number (MathSciNet)
MR3119119

Zentralblatt MATH identifier
1296.47016

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

#### Citation

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. https://projecteuclid.org/euclid.afa/1391614576

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