More Results on Singular Value Inequalities for Compact Operators

ABSTRACT

The well-known arithmetic-geometric mean inequality for singular values, according to Bhatia and Kittaneh, says that if and are compact operators on a complex separable Hilbert space, then Hirzallah has proved that
if are compact operators, then We give inequality which is equivalent to and more general than the
above inequalities, which states that if are compact operators, then

Cite this paper

W. Audeh, "More Results on Singular Value Inequalities for Compact Operators,"*Advances in Linear Algebra & Matrix Theory*, Vol. 3 No. 4, 2013, pp. 27-33. doi: 10.4236/alamt.2013.34006.

W. Audeh, "More Results on Singular Value Inequalities for Compact Operators,"

References

[1] R. Bhatia, “Matrix Analysis, GTM169,” Springer-Verlag, New York, 1997. http://dx.doi.org/10.1007/978-1-4612-0653-8

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

[3] R. Bhatia and F. Kittaneh, “The Matrix Arithmetic-Geometric Mean Inequality Revisited,” Linear Algebra and Its Applications, Vol. 428, 2008, pp. 2177-2191. http://dx.doi.org/10.1016/j.laa.2007.11.030

[4] O. Hirzallah, “Inequalities for Sums and Products of Operators,” Linear Algebra and Its Applications, Vol. 407, 2005, pp. 32-42. http://dx.doi.org/10.1016/j.laa.2005.04.017

[5] W. Audeh, F. Kittaneh, Singular value inequalities for compact operators, Linear Algebra and Its Applications, Vol. 437, 2012, pp. 2516-2522. http://dx.doi.org/10.1016/j.laa.2012.06.032

[6] Y. Tao, “More Results on Singular Value Inequalities of Matrices,” Linear Algebra and Its Applications, Vol. 416, 2006, pp. 724-729. http://dx.doi.org/10.1016/j.laa.2005.12.017

[7] X. Zhan, “Singular Values of Differences of Positive Semidefinite Matrices,” SIAM Journal on Matrix Analysis and Applications, Vol. 22, No. 3, 2000, pp. 819-823. http://dx.doi.org/10.1137/S0895479800369840

[8] R. Bhatia and F. Kittaneh, “The Matrix Arithmetic-Geometric Mean Inequality Revisited,” Linear Algebra and Its Applications, Vol. 428, 2008, pp. 2177-2191. http://dx.doi.org/10.1016/j.laa.2007.11.030

[1] R. Bhatia, “Matrix Analysis, GTM169,” Springer-Verlag, New York, 1997. http://dx.doi.org/10.1007/978-1-4612-0653-8

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

[3] R. Bhatia and F. Kittaneh, “The Matrix Arithmetic-Geometric Mean Inequality Revisited,” Linear Algebra and Its Applications, Vol. 428, 2008, pp. 2177-2191. http://dx.doi.org/10.1016/j.laa.2007.11.030

[4] O. Hirzallah, “Inequalities for Sums and Products of Operators,” Linear Algebra and Its Applications, Vol. 407, 2005, pp. 32-42. http://dx.doi.org/10.1016/j.laa.2005.04.017

[5] W. Audeh, F. Kittaneh, Singular value inequalities for compact operators, Linear Algebra and Its Applications, Vol. 437, 2012, pp. 2516-2522. http://dx.doi.org/10.1016/j.laa.2012.06.032

[6] Y. Tao, “More Results on Singular Value Inequalities of Matrices,” Linear Algebra and Its Applications, Vol. 416, 2006, pp. 724-729. http://dx.doi.org/10.1016/j.laa.2005.12.017

[7] X. Zhan, “Singular Values of Differences of Positive Semidefinite Matrices,” SIAM Journal on Matrix Analysis and Applications, Vol. 22, No. 3, 2000, pp. 819-823. http://dx.doi.org/10.1137/S0895479800369840

[8] R. Bhatia and F. Kittaneh, “The Matrix Arithmetic-Geometric Mean Inequality Revisited,” Linear Algebra and Its Applications, Vol. 428, 2008, pp. 2177-2191. http://dx.doi.org/10.1016/j.laa.2007.11.030