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

## Annals of Functional Analysis

### Volume 5 - Number 1

Article Type: Original Article
Abstract: In this paper we study positive operator monotone functions on (0,1) which have some differences from those on(0,∞): we show that for a concave operator monotone function f on (0,1), the Kwong matrices Kf(s1,,sn)are positive semidefinite for all nn and si(0,1), and f(sp)1/p for p(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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