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الإسم : وسيم عودة

الرتبة العلمية: أستاذ مشارك

المسمى الوظيفي: عضو هيئة تدريسية

المكتب 7212       الرقم الفرعي 7212

بريد الكتروني: waudeh@uop.edu.jo

التخصص: رياضيات

جامعة التخرج: الجامعة الاردنية

تحميل السيرة الذاتية

المؤهل العلمي

    المؤهل العلمي

    الجامعة

    البلد

    سنة الحصول على المؤهل

    الدكتوراه
    الجامعة الاردنية
    الاردن
    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 :الملخص
      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 :الملخص
      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 :الملخص
      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 :الملخص
      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




      :الملخص
      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




      :الملخص
      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




      :الملخص
      We present some general singular value inequalities for Audeh generalized commutator of the form A1X1 +􀀢+ AmXm − Y1B1 −􀀢 − YnBn which provides some recent results for singular value inequalities of commutators due to Audeh, Bhatia-Kittaneh, Kittaneh, Hirzallah-Kittaneh, Hirzallah, and Wang-Du. Download


  • Doctoral Dissertation





      Odeh, W, " Norm inequalities for finite Sums of positive operators " , "",Vol.,No., , Amman, Jordan, 04/16/2009 :الملخص
      In this thesis we prove norm inequalities and singular value inequalities for finite sums of positive operators.
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