Loewner matrices of matrix convex and monotone functions
Fumio HIAI and Takashi SANO
Source: J. Math. Soc. Japan Volume 64, Number 2
(2012), 343-364.
Abstract
The matrix convexity and the matrix monotony of a real C1 function f on (0,∞) are characterized in terms of the conditional negative or positive definiteness of the Loewner matrices associated with f, tf(t), and t2f(t). Similar characterizations are also obtained for matrix monotone functions on a finite interval (a,b).
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Keywords: n-convex; n-monotone; operator monotone; operator convex; Loewner matrix; conditional negative definite; conditional positive definite
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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1335444395
Digital Object Identifier: doi:10.2969/jmsj/06420343
Zentralblatt MATH identifier: 06051240
Mathematical Reviews number (MathSciNet): MR2916071
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