October 2021 More about operator order preserving
Gholamreza Karamali, Hamid Reza Moradi, Mohammad Sababheh
Rocky Mountain J. Math. 51(5): 1691-1699 (October 2021). DOI: 10.1216/rmj.2021.51.1691


It is well known that increasing functions do not preserve operator order in general; nor do decreasing functions reverse operator order. However, operator monotone increasing or operator monotone decreasing functions do. In this article, we employ a convex approach to discuss operator order preserving or conversing functions. As an easy consequence of more general results, we find nonnegative constants γ and ψ such that AB implies

f(B)f(A)+γ1 andf(A)f(B)+ψ1,

for the self-adjoint operators A, B on a Hilbert space with identity operator 1 and for the convex function f whose domain contains the spectra of both A and B.

The connection of these results to the existing literature will be discussed and the significance will be emphasized by some examples.


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Gholamreza Karamali. Hamid Reza Moradi. Mohammad Sababheh. "More about operator order preserving." Rocky Mountain J. Math. 51 (5) 1691 - 1699, October 2021. https://doi.org/10.1216/rmj.2021.51.1691


Received: 10 October 2019; Revised: 21 December 2020; Accepted: 30 December 2020; Published: October 2021
First available in Project Euclid: 17 February 2022

MathSciNet: MR4382992
zbMATH: 07524096
Digital Object Identifier: 10.1216/rmj.2021.51.1691

Primary: 47A63
Secondary: 26A51‎ , 26B25 , 26D15 , ‎39B62

Keywords: Convex functions , Jensen’s inequality , operator order , ‎positive operators , self adjoint operators

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium


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Vol.51 • No. 5 • October 2021
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