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Name : 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, K. Fuad, " Singular Value Inequalities for Compact Operators " , " ELSEVIER",Vol.437,No., Linear algebra and its applications, Amman, Jordan, 06/15/2012 Abstract:
      A singular value inequality due to Bhatia and Kittaneh says that if A and B are compact operators on a complex separable Hilbert space such that A is self-adjoint, B≥0, and ±A≤B, then s_{j}(A)≤s_{j}(B⊕B) for j=1,2,... We give an equivalent inequality, which states that if A,B, and C are compact operators such that [ A B B^{∗} C ]≥0, then s_{j}(B)≤s_{j}(A⊕C) for j=1,2,... Moreover, we give a sharper inequality and we prove that this inequality is equivalent to three equivalent inequalities considered by Tao. In particular, we show that if A and B are compact operators such that A is self-adjoint, B≥0, and ±A≤B, then 2s_{j}(A)≤s_{j}((B+A)⊕(B-A)) for j=1,2,... Some applications of these results will be given. Download




      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


  • 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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