Share This Article:

Singular Value Inequalities for Compact Normal Operators

DOI: 10.4236/alamt.2013.34007    2,603 Downloads   6,783 Views  
Author(s)    Leave a comment


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.

Conflicts of Interest

The authors declare no conflicts of interest.

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.


[1] R. Bhatia, “Matrix Analysis, GTM169,” Springer-Verlag, New York, 1997.
[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.
[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.
[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.
[6] R. Bhatia and F. Kittaneh, “The Matrix Arithmetic-Geometric Mean Inequality Revisited,” Linear Algebra Applications, Vol. 428, 2008, pp. 2177-2191.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.