New characterizations of operator monotone functions
Document Type
Article
Publication Date
6-1-2018
Abstract
If σ is a symmetric mean and f is an operator monotone function on [0,∞), then f(2(A−1+B−1)−1)≤f(AσB)≤f((A+B)/2). Conversely, Ando and Hiai showed that if f is a function that satisfies either one of these inequalities for all positive operators A and B and a symmetric mean different than the arithmetic and the harmonic mean, then the function is operator monotone. In this paper, we show that the arithmetic and the harmonic means can be replaced by the geometric mean to obtain similar characterizations. Moreover, we give characterizations of operator monotone functions using self-adjoint means and general means subject to a constraint due to Kubo and Ando.
Publication Title
Linear Algebra and Its Applications
Volume
546
First Page
169
Last Page
186
Digital Object Identifier (DOI)
10.1016/j.laa.2018.02.004
ISSN
00243795
Citation Information
Dinh, Dumitru, R., & Franco, J. A. (2018). New characterizations of operator monotone functions. Linear Algebra and Its Applications, 546, 169–186. https://doi.org/10.1016/j.laa.2018.02.004