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 ALAMT  Vol.7 No.2 , June 2017
Applications of Arithmetic Geometric Mean Inequality
Abstract: The well-known arithmetic-geometric mean inequality for singular values, due to Bhatia and Kittaneh, is one of the most important singular value inequalities for compact operators. The purpose of this study is to give new singular value inequalities for compact operators and prove that these inequalities are equivalent to arithmetic-geometric mean inequality, the way by which several future studies could be done.
Cite this paper: Audeh, W. (2017) Applications of Arithmetic Geometric Mean Inequality. Advances in Linear Algebra & Matrix Theory, 7, 29-36. doi: 10.4236/alamt.2017.72004.
References

[1]   Bhatia, R. (1997) Matrix Analysis, GTM169. Springer-Verlag, New York.
https://doi.org/10.1007/978-1-4612-0653-8

[2]   Gohberg, I.C. and Krein, M.G. (1969) Introduction to the Theory of Linear Nonselfadjoint Operators. American Mathematical Society, Providence.

[3]   Bhatia, R. and Kittaneh, F. (2008) The Matrix Arithmetic-Geometric Mean Inequality Revisited. Linear Algebra and Its Applications, 428, 2177-2191.
https://doi.org/10.1016/j.laa.2007.11.030

[4]   Audeh, W. and Kittaneh, F. (2012) Singular Value Inequalities for Compact Operators. Linear Algebra and Its Applications, 437, 2516-2522.
https://doi.org/10.1016/j.laa.2012.06.032

[5]   Bhatia, R. and Kittaneh, F. (1990) On the Singular Values of a Product of Operators. SIAM Journal on Matrix Analysis and Applications, 11, 272-277.
https://doi.org/10.1137/0611018

[6]   Zhan, X. (2000) Singular Values of Differences of Positive Semidefinite Matrices. SIAM Journal on Matrix Analysis and Applications, 22, 819-823.
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[7]   Tao, Y. (2006) More Results on Singular Value Inequalities of Matrices. Linear Algebra and Its Applications, 416, 724-729.
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