Singular Value Inequalities for Compact Normal Operators

ABSTRACT

We give singular value inequality to compact normal operators, which states that if is compact normal operator on a complex separable Hilbert space, where is the cartesian decomposition of , then Moreover, we give inequality which asserts that if is compact* *normal operator, then .Several inequalities will be
proved.

We give singular value inequality to compact normal operators, which states that if is compact normal operator on a complex separable Hilbert space, where is the cartesian decomposition of , then Moreover, we give inequality which asserts that if is compact

Cite this paper

W. Audeh, "Singular Value Inequalities for Compact Normal Operators,"*Advances in Linear Algebra & Matrix Theory*, Vol. 3 No. 4, 2013, pp. 34-38. doi: 10.4236/alamt.2013.34007.

W. Audeh, "Singular Value Inequalities for Compact Normal 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] W. Audeh and F. Kittaneh, “Singular Value Inequalities for Compact Operators,” Linear Algebra Applications, Vol. 437, 2012, pp. 2516-2522. http://dx.doi.org/10.1016/j.laa.2012.06.032

[4] 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

[5] O. Hirzallah and F. Kittaneh, “Inequalities for Sums and Direct Sums of Hilbert Space Operators,” Linear Algebra Applications, Vol. 424, 2007, pp. 71-82. http://dx.doi.org/10.1016/j.laa.2006.03.036

[6] R. Bhatia and F. Kittaneh, “The Matrix Arithmetic-Geometric Mean Inequality Revisited,” Linear Algebra 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] W. Audeh and F. Kittaneh, “Singular Value Inequalities for Compact Operators,” Linear Algebra Applications, Vol. 437, 2012, pp. 2516-2522. http://dx.doi.org/10.1016/j.laa.2012.06.032

[4] 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

[5] O. Hirzallah and F. Kittaneh, “Inequalities for Sums and Direct Sums of Hilbert Space Operators,” Linear Algebra Applications, Vol. 424, 2007, pp. 71-82. http://dx.doi.org/10.1016/j.laa.2006.03.036

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