W. Audeh, " More Results on Singular Value Inequalities for Compact Normal Operators " , "Scientific Research Publishing",Vol.10,No., Advances in linear algebra and matrix theory, Amman, Jordan, 03/15/2013
Abstract:
The wellknown arithmeticgeometric mean inequality for singular values, due to Bhatia and Kittaneh says that if A and B are compact operators on a complex separable Hilbert space, then
2s_j (AB^* )≤s_j (A^* A+B^* B)
for j=1,2,... Hirzallah has proved that if A₁,A₂,A₃,and A₄ are compact operators, then
√2 s_j (A_1 A_2^*+A_3 A_4^* ^(1/2) )≤s_j ([■(A_1&A_3@A_2&A_4 )] )
for j=1,2,...We give inequality which is equivalent to and more general than the above inequalities, which states that if A_(i,),B_i,i=1,2,…,n are compact operators, then
2s_j (A_1 B_1^*+A_2 B_2^*+⋯+A_n B_n^* )≤s_j [■(A_1&A_2&⋯&A_n@0&0&⋯&0@⋮&⋮&⋮&⋮@0&0&0&0)^2+■(B_1&B_2&⋯&B_n@0&0&⋯&0@⋮&⋮&⋮&⋮@0&0&0&0)^2 ]
for j=1,2,...
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W. Audeh, " Singular Value Inequalities for Compact Normal Operators " , "Scientific Research Publishing",Vol.10,No., Advances in linear algebra and matrix theory, Amman, Jordan, 03/20/2013
Abstract:
We give singular value inequality to compact normal operators, which states that if A is compact normal operator on a complex separable Hilbert space, where A=A_1+iA_2 is the cartesian decomposition of A, then
1/√2 s_j (A_1+A_2)≤s_j (A)≤s_j (A_1 +A_2 )
for j=1,2,... Moreover, we give inequality which asserts that if A is compact normal operator, then
√2 s_j (A_1+A_2)≤s_j (A+iA^*)≤2s_j (A_1+A_2)
for j=1,2,... Several inequalities will be proved.
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W. Audeh, " More Commutator Inequalities for Hilbert Space Operators " , "Pushpa Publishing House",Vol.,No., International Journal of Functional Analysis, Operator Theory and Matrices, Allahabad, India, 06/12/2014
Abstract:
We present general singular value inequalities for nth order Audeh generalized commutator from them recent results for commutators due to BhatiaKittaneh, Kittaneh, HirzallahKittaneh, Hirzallah, and WangDu. are special cases. Several applications are given.
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Wasim Audeh and Manal Alabadi, " More numerical radius inequalities for operator matrices " , "international journal of pure and applied mathematics",Vol.,No., Academic publications, , 04/15/2018
Abstract:
In this work, we will prove several numerical radius inequalities from them we get
recently proved numerical radius inequalities as special cases, and we will present numerical
radius inequalities which are sharper than recently proved numerical radius inequalities.
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Wasim Audeh, " Applications of Arithmetic Geometric Mean Inequality " , "Advances in Linear Algebra and Matrix Theory",Vol.,No., Alamt, , 07/15/2017
Abstract:
The wellknown arithmeticgeometric 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 ineq
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Wasim Audeh, " Numerical radius inequalities for sums and products of operators " , "Advances in Linear Algebra and Matrix theory",Vol.9,No., Alamt, China, 07/10/2019
Wasim Audeh, " Generalizations for singular value inequalities of operators " , "Advances of operator theory",Vol.Online,No., Springer, America, 01/01/2020
Abstract:
This paper proves singular value inequality, from which wellknown singular value
and norm inequalities are special cases: Let A, B, and X are positive operators on a
complex separable Hilbert space. Then
s j
A1/2XA1/2 + B1/2XB1/2
≤ s j
A1/2XA1/2 +
B1/2XA1/2
⊕
B1/2
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Wasim Audeh, " Generalizations for singular value and arithmeticgeometric mean inequalities " , "مجله",Vol.489,No., Elsevier, America, 04/20/2020
Abstract:
Among other results, we have provided general singular value inequality as follows:
Let X1, X2, Y1, and Y2be positive bounded linear operators on a complex separable Hilbert space. Then
2sj
X
1/2
1 Y
1/2
1 − X
1/2
2 Y
1/2
2
≤ sj (S ⊕ T)
for j=1, 2, ..., where S=X1+Y1+X1/22X1/21
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Ahmad AlNatoor, Wasim Audeh and Fuad Kittaneh, " Norm inequalities of DavidsonPower Type " , "Mathematical Inequalities and Applications",Vol.23,No., EleMath, Croatia, 04/15/2020
Abstract:
Let A,B, and X be n×n complex matrices such that A and B are positive semidefinite. It is shown, among other inequalities, that AX+XB 1 2 max(A,XBX∗)+ 1 2 max(X∗AX,B)+ A1/2XB1/2 . This norm inequality extends an inequality of Kittaneh, which improves an earlier inequality of Da
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Odeh, W, " Norm inequalities for finite Sums of positive operators " , "",Vol.,No., , Amman, Jordan, 04/16/2009
Abstract:
In this thesis we prove norm inequalities and singular value inequalities for finite sums of positive operators.

