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Name : Dr. Wasim Odeh

Academic Rank: Associate Professor

Administrative Position : Faculty Academic Member

Office 7212       Ext No 7212

Email : waudeh@uop.edu.jo

Specialization: Mathematics

Graduate Of: University of Jordan

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Qualification

    Qualification

    University

    Country

    Year

    Ph.D
    University of Jordan
    Jordan
    2009



  • Journal Paper





      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 well-known arithmetic-geometric 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,... Download




      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. Download




      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 Bhatia-Kittaneh, Kittaneh, Hirzallah-Kittaneh, Hirzallah, and Wang-Du. are special cases. Several applications are given. Download




      Wasim Audeh and Manal A-labadi, " 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. Download




      Wasim Audeh, " Applications of Arithmetic Geometric Mean Inequality " , "Advances in Linear Algebra and Matrix Theory",Vol.,No., Alamt, , 07/15/2017 Abstract:
      The well-known arithmetic-geometric 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 Download




      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 well-known 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 Download




      Wasim Audeh, " Generalizations for singular value and arithmetic-geometric 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 Download




      Ahmad Al-Natoor, Wasim Audeh and Fuad Kittaneh, " Norm inequalities of Davidson-Power Type " , "Mathematical Inequalities and Applications",Vol.23,No., Ele-Math, 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 Download


  • Doctoral Dissertation





      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.
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