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	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).