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Singular Value Inequalities for Compact Normal Operators
Department of Basic Sciences, Petra University, Amman, Jordan
- 1 Department of Basic Sciences, Petra University, Amman, Jordan
Advances in Linear Algebra & Matrix Theory·Volume 03 (2013)·Pages 34–38·Published 6 December 2013·DOI10.4236/alamt.2013.34007
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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.
KeywordsCompact OperatorInequalityNormal OperatorSelf-Adjoint OperatorSingular Value
- R. Bhatia, “Matrix Analysis, GTM169,” Springer-Verlag, New York, 1997. http://dx.doi.org/10.1007/978-1-4612-0653-8
- I. C. Gohberg and M. G. Krein, “Introduction to the Theory of Linear Nonselfadjoint Operators,” American Mathematical Society, Providence, 1969.
- 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
- 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
- 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
- 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