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Operator Theory (AN9): Διαφορά μεταξύ των αναθεωρήσεων

Operator Theory (AN9): Διαφορά μεταξύ των αναθεωρήσεων

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(Νέα σελίδα με 'Graduate Courses Outlines - [https://math.uoi.gr Department of Mathematics] === General === {| class="wikitable" |- ! School | School of Science |- ! Academic Unit | Department of Mathematics |- ! Level of Studies | Graduate |- ! Course Code | ΧΧΧ |- ! Semester | 000 |- ! Course Title | ΧΧΧ |- ! Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |- ! Course Type | General Background |- ! Prerequisite Courses | - |- ! L...')
 
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(8 ενδιάμεσες αναθεωρήσεις από τον ίδιο χρήστη δεν εμφανίζεται)
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[[Graduate Courses Outlines]] - [https://math.uoi.gr  Department of Mathematics]
* [[Θεωρία Τελεστών (AN9)|Ελληνική Έκδοση]]
{{Course-Graduate-Top-EN}}
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=== General ===
=== General ===
Γραμμή 15: Γραμμή 17:
|-
|-
! Course Code
! Course Code
| ΧΧΧ
| AN9
|-
|-
! Semester
! Semester
| 000
| 2
|-
|-
! Course Title
! Course Title
| ΧΧΧ
| Operator Theory
|-
|-
! Independent Teaching Activities
! Independent Teaching Activities
Γραμμή 27: Γραμμή 29:
|-
|-
! Course Type
! Course Type
| General Background
| Specialized general knowledge
|-
|-
! Prerequisite Courses
! Prerequisite Courses
| -
| Functional Analysis
|-
|-
! Language of Instruction and Examinations
! Language of Instruction and Examinations
|
|
ΧΧΧ
Greek
|-
|-
! Is the Course Offered to Erasmus Students
! Is the Course Offered to Erasmus Students
| Yes
| Yes (in English)
|-
|-
! Course Website (URL)
! Course Website (URL)
Γραμμή 49: Γραμμή 51:
! Learning outcomes
! Learning outcomes
|
|
ΧΧΧ
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
! General Competences
|
|
ΧΧΧ
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 ===
=== Syllabus ===


ΧΧΧ
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 ===
=== Teaching and Learning Methods - Evaluation ===
Γραμμή 66: Γραμμή 68:
! Delivery
! Delivery
|
|
ΧΧΧ
Teaching on the blackboard
|-
|-
! Use of Information and Communications Technology
! Use of Information and Communications Technology
|
|
ΧΧΧ
Communication with the students via e-mail
|-
|-
! Teaching Methods
! Teaching Methods
Γραμμή 81: Γραμμή 83:
| 39
| 39
|-
|-
| ΧΧΧ
| Individual study
| 000
| 78
|-
|-
| ΧΧΧ
| Resolving exercises and assignments
| 000
| 70.5
|-
|-
| Course total  
| Course total  
Γραμμή 93: Γραμμή 95:
! Student Performance Evaluation
! Student Performance Evaluation
|
|
ΧΧΧ
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).
|}
|}


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Τελευταία αναθεώρηση της 16:26, 15 Ιουνίου 2023

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.
Ανακτήθηκε από «https://wiki.math.uoi.gr/index.php?title=Operator_Theory_(AN9)&oldid=4651»