Syllabus
M581 Functional Analysis I 3 credit units
Normed spaces, Banach spaces, continuous linear operators, Hahn-Banach theorem, Duality, the open mapping theorem. The closed graph theorem, the uniform boundedness theorem, Hilbert spaces, Adjoint operators, unitary and normal operators, projections, spectral theory in finite dimensional spaces, spectral properties of bounded linear operators.
Syllabus
COURSE MATH 581
SEMESTER II, 1428 – 1429 H
Department of Mathematics
TEXT BOOK: Functional Analysis, MCGraw Hill. 1973
Authors: J.Rudin(3rd edition)
Week Course Details
1. Normed spaces,
2. Banach spaces,
3. continuous linear operators,
4. Hahn-Banach theorem,
5. Duality, the open mapping theorem.
6. The closed graph theorem, the uniform boundedness theorem,
7. Hilbert spaces,
8. Adjoint operators,
9. unitary and normal operators,
10. projections,
11. spectral theory in finite dimensional spaces,
12. spectral properties of bounded linear operators.
13. Spectral properties examples and application
14.Spectrum radius
15.
Revision.
COMMING EXAMS:
Mid-Term Exam 1: 19/04/1429 From: 7 to 8.30 (Done)
Mid-Term Exam 2: 20/05/1429 From: 7 to 8.30 (Done)
Final Exam: 19/06/1429: From: 1 to 4.00 (PM)
تقيم تقسيم الدرجات:
§ اختبار الفصل الأول: 20
§ اختبار الفصل الثاني: 20
§ درجات التمارين: 10
§ الامتحان النهائي: 50
Lecture
Exercises With Solutions