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M582              Functional Analysis (II)        3 credit units

Syllabus:  Compact linear operators and their spectral properties. Spectral properties  of bounded, self-adjoint operators, spectral family of a bounded self-adjoint operator.  Spectral representation of bounded self-adjoint operators.  Banach Algebras,  Spectral theory in Banach algebra.  Commutative Banach Algebras.  Gelfand Mapping.  Spectral theorem for normal operators.

Syllabus

COURSE MATH 582

SEMESTER II, 1428 – 1429 H

Department of Mathematics

TEXT BOOK:

  • Murphy, C*-Algebras in operator theory.
  • Rudin, Functional Analysis, McGraw-Hill 1973.
  • R.G. Douglas, Banach Algebra techniques in operator theory, Academic Press 1972.
  • E.R. Lorch, Spectral Theory, University Text in the Mathematical Sciences, New York. Oxford University Press 1962.
  • E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley & Sons,1978
  • Week Course Details

    1. Compact linear operators

    2. Spectral properties.

    3. Spectral properties  of bounded, self-adjoint operators,

    4. Spectral family of a bounded self-adjoint operator. 

    5. Spectral representation of bounded self-adjoint operators. 

    6. Banach Algebras, 

    7. Spectral theory in Banach algebra. 

    8. Commutative Banach Algebras. 

    9. Gelfand Mapping. 

    10. Spectral theorem for normal operators.

    11. Compact normal operator

    12. Spectral properties of normal operators

    13. Trace class operators and their properties

    14. Examples and applications

    15. Revision.

     COMMING EXAMS:

     Mid-Term Exam 1: 21/04/1429 From: 7 to 8.30 (Done)

    Mid-Term Exam 2:  22/05/1429 From: 7 to 8.30 (Done)

     

    Final Exam: 23/06/1429: From: 1 to 4.00 (PM)

     

       تقيم    تقسيم  الدرجات:

    §         اختبار الفصل الأول: 20

    §         اختبار الفصل الثاني: 20

    §         درجات التمارين: 10

    §         الامتحان النهائي: 50

     

     

     

      Lecture1

      Lecture2

      Problem1

      Problem2

       
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