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