Information Package / Course Catalogue
C*-Algebras
Course Code: MTK524
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 8
Objectives of the Course

The course aim to introduce C*-algebras by giving the basic definition and theorems of C*-algebras.

Course Content

The definition and examples of C*-algebras, commutative C*-algebras, quotient C*-algebras, representations, the dual of a C*-algebra, automorphisms of C*-algebras.

Name of Lecturer(s)
Prof. Hülya İNCEBOZ
Learning Outcomes
1.Ability to understand the concept of C*-algebra, its basic properties and ability to recognize the examples of some C*-algebras.
2.Ability to understand the concept of a functional on C*-algebras.
3.Ability to understand quotient C*-algebras.
4.Ability to find the dual of a C*-algebra.
5.Ability to find automorphisms of C*-algebras.
Recommended or Required Reading
1.C*-Algebras and Operator Theory, Gerald J. Murphy, Academic Press Inc., San Diego, 1990.
2.C*-Algebras and W*-Algebras, S. Sakai, Springer-Verlag, New York, 1970.
Weekly Detailed Course Contents
Week 1 - Theoretical
Involute algebras and normed involute algebras
Week 2 - Theoretical
C*-algebras
Week 3 - Theoretical
Commutative C*-algebras
Week 4 - Theoretical
Examination of a functional on C*-algebras and approximation to identity
Week 5 - Theoretical
Quotient C*-algebras
Week 6 - Theoretical
Representations
Week 7 - Theoretical
Envelop of C*-algebras
Week 8 - Theoretical
Ideals of C*-algebras
Week 9 - Theoretical
Dual of a C*-algebra
Week 10 - Theoretical
Polar decomposition of a linear mapping
Week 11 - Theoretical
Positive part of the ideal of a C*-algebra and its tensor products
Week 12 - Theoretical
Automorphisms of C*-algebras
Week 13 - Theoretical
Inner automorphism
Week 14 - Theoretical
Derivable automorphism
Assessment Methods and Criteria
Type of AssessmentCountPercent
Final Examination1%70
Assignment2%30
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory143384
Assignment216236
Individual Work140228
Final Examination150252
TOTAL WORKLOAD (hours)200
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
OÇ-1
3
4
4
3
3
4
3
3
4
4
OÇ-2
4
4
4
4
3
4
3
3
3
4
4
OÇ-3
4
4
5
5
3
4
3
3
4
4
OÇ-4
5
4
5
5
4
4
3
3
3
4
4
OÇ-5
5
4
5
4
4
4
3
3
3
4
4
Adnan Menderes University - Information Package / Course Catalogue
2026