Loewner matrices of matrix convex and monotone functions

• Hiai Fumio

  Graduate School of Information Sciences, Tohoku University

• Sano Takashi

  Department of Mathematical Sciences, Faculty of Science, Yamagata University

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).

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 64 (2), 343-364, 2012

  The Mathematical Society of Japan

Keywords

• <i>n</i>-convex
• <i>n</i>-monotone
• operator monotone
• operator convex
• Loewner matrix
• conditional negative definite
• conditional positive definite

Details

• CRID: 1390282680093134464
• NII Article ID: 10030740187
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/06420343
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL BIB ID: 023596682
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I023596682
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed