Reverse and improved inequalities for operator monotone functions

Sever Dragomir

Abstract


In this paper we provide several refinements and reverse operator inequalities for operator monotone functions in Hilbert spaces. We also obtain refinements and a reverse of Lowner-Heinz celebrated inequality that holds in the case of power function.

Keywords


Operator monotone functions; Lowner-Heinz inequality; logarithmic operator inequality

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References


Bhatia, R., Matrix Analysis. Graduate Texts in Mathematics, 169. Springer-Verlag, New York, 1997.

Fujii, J. I., Seo, Y., On parametrized operator means dominated by power ones, Sci. Math. 1 (1998), 301–306.

Furuta, T., Concrete examples of operator monotone functions obtained by an elementary method without appealing to Lowner integral representation, Linear Algebra Appl. 429 (2008), 972–980.

Furuta, T., Precise lower bound of f(A)-f(B) for A > B > 0 and non-constant operator monotone function f on [0,infty), J. Math. Inequal. 9 (1) (2015), 47–52.

Heinz, E., Beitrage zur Storungsteorie der Spektralzerlegung, Math. Ann. 123 (1951), 415–438.

Lowner, K., Uber monotone Matrixfunktionen, Math. Z. 38 (1934), 177–216.

Kubo, F., Ando, T., Means of positive linear operators, Math. Ann. 246 (1980), 205–224.

Moslehian, M. S., Najafi, H., An extension of the Lowner–Heinz inequality, Linear Algebra Appl. 437 (2012), 2359–2365.

Zuo, H., Duan, G., Some inequalities of operator monotone functions, J. Math. Inequal. 8 (4) (2014), 777–781.




DOI: http://dx.doi.org/10.17951/a.2020.74.2.19-29
Date of publication: 2020-12-28 17:41:56
Date of submission: 2020-12-27 16:38:28


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