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| MATL7860 | Sub-Normal Operators | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | -- | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of this course is the introduction of subnormal operators and, teaching knowledge on this operator class. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | 1, 5, 2, 6 | | | | PO - 2 : | 1, 5, 4 | | | | PO - 3 : | 1, 5, 6, 4 | | | | PO - 4 : | 1, 5, 6, 4,3 | | | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Basic concepts of subnormal operators, Hilbert-Schmidt operators, isometries, shift operators, definition and properties of quasinormal and hyponormal operators, pure operators and the minimal normal extensions. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Trace class and Hilbert-Schmidt operators, Some topologies on B(H) | | | Week 2 | Isometries and shift operators | | | Week 3 | Direct sums | | | Week 4 | Definition and examples of subnormal operators | | | Week 5 | Pure operators and the minimal normal extension | | | Week 6 | Quasinormal and hyponormal operators | | | Week 7 | Cyclic subnormal operators and weighted shifts operators | | | Week 8 | Applications | | | Week 9 | Middle Exam | | | Week 10 | Bounded point evaluations | | | Week 11 | Bergman operators and spectral sets | | | Week 12 | The commutant of a subnormal operator | | | Week 13 | The restriction algebra and the functional calculus | | | Week 14 | The C^*-algera generated by a subnormal operator | | | Week 15 | Unitary equivalence, similarity and quasisimilarity | | | Week 16 | Applications | | | |
| 1 | Conway J.B. The Theory of Subnormal Operators, AMS Surveys and Monographs v. 36, 1985 | | | |
| 1 | Conway J.B. A Course in Functional Anatysis, 2 nd ed., Springer-Verlag New York Inc, 1990 | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 20/11/2015 | 2,00 | 50 | | End-of-term exam | 16 | 08/01/2016 | 2,00 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 8 | 14 | 112 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 20 | 1 | 20 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 188 |
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