Operator Theory (AN9)

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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
Activity Semester Workload
Lectures 39
Individual study 78
Resolving exercises and assignments 70.5
Course total 187.5
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.