COMPARISONS OF HEINZ OPERATOR MEANS WITH DIFFERENT PARAMETERS

Aliaa Abed Al-Jawwad Burqan

doi:10.22452/mjs.sp2019no1.3

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Published: Feb 28, 2019

DOI: https://doi.org/10.22452/mjs.sp2019no1.3

Keywords:

Heinz means positive operator unitarily invariant norm inequality monotonicity principle

Aliaa Abed Al-Jawwad Burqan

Zarqa University

Abstract

This article aims to present new comparisons of Heinz operator means with different parameters by the help of appropriate scalar comparisons and the monotonicity principle for bounded self-adjoint Hilbert space operators. In particular, for any positive operators, we establish the inequality

$H{\tau }(A,B)\leq \left ( 1-\frac{(1-2\mu )^{2}}{(1-2\tau )^{2}} \right )(A\bigtriangledown B)+\frac{(1-2\mu )^{2}}{(1-2\tau )^{2}} H{\mu }(A,B),$

where $\mu ,\tau \epsilon [0,1]$ satisfying

$\tau \neq \frac{1}{2},\left | \tau -\frac{1}{2} \right |\geq \left | \mu -\frac{1}{2} \right | and \left | 2\tau -1 \right |+\left | 2\mu -1 \right |\leq 1$

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How to Cite

Burqan, A. A. A.-J. (2019). COMPARISONS OF HEINZ OPERATOR MEANS WITH DIFFERENT PARAMETERS. Malaysian Journal of Science, 38(Sp 1), 33–42. https://doi.org/10.22452/mjs.sp2019no1.3

Issue

Vol. 38 No. Sp 1 (2019): Special Issue 3rd International Conference of Mathematical Sciences and Statistics (ICMSS2018)

Section

ICMSS2018 (Published)

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References

Bhatia R. and Davis C. (1993). More matrix forms of the arithmetic-geometric mean inequality. SIAM Journal on Matrix Analysis and Applications 14: 132-136.

Bhatia R. (2006). Interpolating the arithmetic-geometric mean inequality and its operator version. Linear Algebra and its Applications 413: 355-363.

Kittaneh F. (2010). On the convexity of the Heinz means. Integral Equations and Operator Theory 68: 519-527.

Kittaneh F., KrniÄ‡ M., LovriÄeviÄ‡ N. and PeÄariÄ‡ J. (2012). Improved arithmetic-geometric and Heinz means inequalities for Hilbert space operators. Publicationes Mathematicae Debrecen 80: 465-478.

Kittaneh F.and KrniÄ‡ M. (2013). Refined Heinz operator inequalities. Linear and Multilinear Algebra 61: 1148-1157.

Kittaneh F. and Manasrah Y. (2010). Improved young and Heinz inequalities for matrices. Journal of Mathematical Analysis and Applications 361: 262-269.

Kittaneh F. and Manasrah Y. (2011). Reverse Young and Heinz inequalities for matrices. Linear and Multilinear Algebra 59: 1031-1037.

PeÄariÄ‡ J. , Furuta T., MiÄ‡iÄ‡ Hot J. and Seo Y. ( 2005). Mond-PeÄariÄ‡ Method in Operator Inequalities. Inequalities for bounded selfadjoint operators on a Hilbert space. Monographs in Inequalities, 1. Zagreb: Element.

Zhan X. (1998). Inequalities for unitarily invariant norms. SIAM Journal on Matrix Analysis and Applications 20: 466-470.

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