Operator Theory (AN9)
Graduate Courses Outlines - Department of Mathematics
General
| School | School of Science |
|---|---|
| Academic Unit | Department of Mathematics |
| Level of Studies | Graduate |
| Course Code | AN9 |
| Semester | 2 |
| Course Title | Operator Theory |
| Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
| Course Type | Specialized general knowledge |
| Prerequisite Courses | Functional Analysis |
| Language of Instruction and Examinations |
Greek |
| Is the Course Offered to Erasmus Students | Yes (in English) |
| Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
The aim of this course is for postgraduate students to acquire a special background in Operator Theory in general Banach spaces and in particular in Hilbert spaces |
|---|---|
| General Competences |
The course aims to enable the graduate student to acquire the ability to analyze and synthesize advanced concepts of Operator Theory. The goal is to acquire the resources for independent and group work in an interdisciplinary environment. |
Syllabus
Bounded linear operators on Banach spaces and Hilbert spaces. Spectrum of an operator, the spectrum of a self-adjoint operator. Functions of self-adjoint operators, spectral theorem. Topologies in operator spaces.
Teaching and Learning Methods - Evaluation
| Delivery |
Teaching on the blackboard | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology |
Communication with the students via e-mail | ||||||||||
| Teaching Methods |
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| Student Performance Evaluation |
Written exam at the end of the semester (mandatory), delivery of assignments and exercises during the semester (mandatory), lecture-presentation on the board by the student (optional). |
Attached Bibliography
- Y. Abramovic C. Aliprantis, An invitation to Operator Theory.
- J. Conway, A course in Functional Analysis.
- R. Douglas, Banach Algebra Techniques in Operator Theory.
- V. Sunder Functional Analysis, Spectral Theory.
- W. Rudin Functional Analysis.