Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2018;2018(1):164.
doi: 10.1186/s13660-018-1758-z. Epub 2018 Jul 5.

Reverses of Ando's and Hölder-McCarty's inequalities

Monire Hajmohamadi  1 , Rahmatollah Lashkaripour  1 , Mojtaba Bakherad  1
Affiliations

Reverses of Ando's and Hölder-McCarty's inequalities

Monire Hajmohamadi et al. J Inequal Appl. 2018.

Abstract

In this paper, we give some reverse-types of Ando's and Hölder-McCarthy's inequalities for positive linear maps, and positive invertible operators. For this purpose, we use a recently improved Young inequality and its reverse.

Keywords: Ando’s inequality; Hölder–McCarthy’s inequality; Positive operator; Young inequality.

PubMed Disclaimer

Conflict of interest statement

The authors declare that they have no competing interests.

References

    1. Ando T. Concavity of certain maps on positive definite matrices and applications to Hadamard products. Linear Algebra Appl. 1979;27:203–241. doi: 10.1016/0024-3795(79)90179-4. - DOI
    1. Bakherad M., Krnić M., Moslehian M.S. Reverse Young-type inequalities for matrices and operators. Rocky Mt. J. Math. 2016;46(4):1089–1105. doi: 10.1216/RMJ-2016-46-4-1089. - DOI
    1. Bakherad M., Lashkaripour R., Hajmohamadi M. Extensions of interpolation between the arithmetic–geometric mean inequality for matrices. J. Inequal. Appl. 2017;2017:209. doi: 10.1186/s13660-017-1485-x. - DOI - PMC - PubMed
    1. Bhatia R. Positive Definite Matrices. Princeton: Princeton University Press; 2007.
    1. Fujii M., Lee E.-Y., Seo Y. A defference counterpart to a matrix Hölder inequality. Linear Algebra Appl. 2010;432:2565–2571. doi: 10.1016/j.laa.2009.12.002. - DOI

LinkOut - more resources