Graduate Courses Outlines - Department of Mathematics
General
| School
|
School of Science
|
| Academic Unit
|
Department of Mathematics
|
| Level of Studies
|
Graduate
|
| Course Code
|
AN4
|
| Semester
|
1
|
| Course Title
|
Functional Analysis
|
| Independent Teaching Activities
|
Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
|
| Course Type
|
General Background
|
| Prerequisite Courses
|
-
|
| 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 objectives of the course are: The acquisition of background from the students on the basic structures and techniques of Functional Analysis, as independent knowledge as well as a tool for the other branches of Analysis, so that they will have the potential to apply the knowledge they get in applications.
|
| General Competences
|
The course aims to give the postgraduate student the ability to analyse and synthesize advanced concepts of Functional Analysis. The goal is to acquire the skills for autonomous work and teamwork in an interdisciplinary environment and to able to produce new research ideas.
|
Syllabus
- Normes spaces, Banach spaces and Hilbert spaces, classical examples (sequence spaces and function spaces). Basic theorems.
- General theory of topological vector spaces, locally convex spaces, separation theorems.
- Weak topologies, theorems of Mazur, Alaoglu and Goldstine, weak compactness.
- Schauder bases and basic sequences.
- Extreme points, Krein Milman theorem.
- Riesz representation theorem, Lp spaces.
- Fixed point theorems.
Teaching and Learning Methods - Evaluation
| Delivery
|
Face to face
|
| Use of Information and Communications Technology
|
-
|
| Teaching Methods
|
| Activity
|
Semester Workload
|
| Lectures
|
39
|
| Study and analysis of bibliography
|
78
|
| Preparation of assignments and interactive teaching
|
70.5
|
| Course total
|
187.5
|
|
| Student Performance Evaluation
|
Written examination at the end of the semester.
|
Attached Bibliography
- Habala, Hajek, Zizler, Introduction to Banach Spaces I and II.
- W. Rudin, Functional Analysis.
- J. Lindenstrauss, L. Tzafriri, Banach spaces I.
- F. Albiac, N. Kalton, Topics in Banach Space theory.
- Νεγρεπόντης, Ζαχαριάδης, Καλαμίδας, Φαρμάκη, Γενική Τοπολογία και Συναρτησιακή Ανάλυση.