# صالح احمد محمد مشرى

 This Site: صالح احمد محمد مشرى

Guidelines_English_Final

### Quick Launch

 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