Skip to main content

A Survey on Operator Monotonicity, Operator Convexity, and Operator Means

  • Chansangiam P
Citations of this article
Mendeley users who have this article in their library.


This paper is an expository devoted to an important class of real-valued functions introduced by Löwner, namely, operator monotone functions. This concept is closely related to operator convex/concave functions. Various characterizations for such functions are given from the viewpoint of differential analysis in terms of matrix of divided differences. From the viewpoint of operator inequalities, various characterizations and the relationship between operator monotonicity and operator convexity are given by Hansen and Pedersen. In the viewpoint of measure theory, operator monotone functions on the nonnegative reals admit meaningful integral representations with respect to Borel measures on the unit interval. Furthermore, Kubo-Ando theory asserts the correspondence between operator monotone functions and operator means.




Chansangiam, P. (2015). A Survey on Operator Monotonicity, Operator Convexity, and Operator Means. International Journal of Analysis, 2015, 1–8.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free