Open Access
2014 Kwong matrices and operator monotone functions on $(0,1)$
Juri Morishita, Takashi Sano, Shintaro Tachibana
Ann. Funct. Anal. 5(1): 121-127 (2014). DOI: 10.15352/afa/1391614576


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.


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Juri Morishita. Takashi Sano. Shintaro Tachibana. "Kwong matrices and operator monotone functions on $(0,1)$." Ann. Funct. Anal. 5 (1) 121 - 127, 2014.


Published: 2014
First available in Project Euclid: 5 February 2014

zbMATH: 1296.47016
MathSciNet: MR3119119
Digital Object Identifier: 10.15352/afa/1391614576

Primary: 47A63
Secondary: 15B48

Keywords: Kwong matrix , Loewner matrix , operator monotone function , positive semidefinite

Rights: Copyright © 2014 Tusi Mathematical Research Group

Vol.5 • No. 1 • 2014
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