Loewner matrices of matrix convex and monotone functions

Fumio Hiai; Takashi Sano

doi:10.2969/jmsj/06420343

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

Loewner matrices of matrix convex and monotone functions

Fumio Hiai, Takashi Sano

著者情報

キーワード: n-convex, n-monotone, operator monotone, operator convex, Loewner matrix, conditional negative definite, conditional positive definite

ジャーナルフリー

2012 年 64 巻 2 号 p. 343-364

DOI https://doi.org/10.2969/jmsj/06420343

詳細

抄録

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).