Understanding the structure theories of partially ordered structures, Riesz spaces and Banach lattices, and positive operators defined on these spaces.
Prerequisite(s)
MBY0023 General Topology and MBY0022 Methods of Functional Analysis
Corequisite(s)
None
Special Requisite(s)
Proficiency in English, enough to be able to follow graduate texts in Mathematics.
Instructor(s)
Professor Mert ÇAĞLAR
Course Assistant(s)
None
Schedule
Will be announced in the forthcoming term.
Office Hour(s)
Assoc. Prof. Dr. Mert ÇAĞLAR, AK/3-A-03/05
Teaching Methods and Techniques
-Lecture and homeworks.
Principle Sources
-C.D. Aliprantis & O. Burkinshaw, Positive Operators, Springer, The Netherlands, 2006.
Other Sources
-Y.A. Abramovich & C.D. Aliprantis, An Invitation to Operator Theory, American Mathematical Society,
GSM, Vol. 50, Providence, RI, 2002.
-H.H. Schaefer, Banach Lattices and Positive Operators, Springer-Verlag, New York, Heidelberg, Berlin,
1974.
-A.C. Zaanen, Introduction to Operator Theory in Riesz Spaces, Springer-Verlag, Berlin, Heidelberg,
1997.
Course Schedules
Week
Contents
Learning Methods
1. Week
Basic properties of positive operators I
Lecture and homework
2. Week
Basic properties of positive operators II
Lecture and homework
3. Week
Extensions of positive operators
Lecture and homework
4. Week
Order projections
Lecture and homework
5. Week
Order-continuous operators I
Lecture and homework
6. Week
Order-continuous operators II
Lecture and homework
7. Week
Positive linear functionals I
Lecture and homework
8. Week
Midterm Exam
Midterm Exam
9. Week
Positive linear functionals II
Lecture and homework
10. Week
Components of a positive operator
Lecture and homework
11. Week
Order homomorphisms I
Lecture and homework
12. Week
Order homomorphisms II
Lecture and homework
13. Week
Orthomorphisms I
Lecture and homework
14. Week
Orthomorphisms II
Lecture and homework
15. Week
Final Exam Week
Final Exam
16. Week
Final Exam Week
Final Exam
17. Week
Final Exam Week
Final Exam
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
30
Homework / Term Projects / Presentations
7
30
Final Exam
1
40
Program Outcomes
PO-1
Have ability to develop new mathematical ideas and methods by using high-level mental processes such as creative and critical thinking, problem solving and decision-making.
PO-2
Follow the current developments in the field of mathematics, and make the critical analysis, synthesis and evaluation of new and complex ideas.
PO-3
Understand the interdisciplinary interaction related to Mathematics and play a role in an effective manner in environments that require with the resolution of problems encountered in this process.
PO-4
Defend original views on the discussion of the issues in the field of mathematics with experts and communicate to show competence in oral and written.
PO-5
Do research with high-level national and international scientific working groups, and acquire the responsibility to contribute to the literature by publishing original works in respected scientific journals.
PO-6
Use computer software to solve problems effectively by following the developments in information and communication technologies.
PO-7
Contribute to the solution of social, scientific, cultural and ethical problems encountered issues related to the field and support the development of these values.
PO-8
To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-9
Establish and discuss in written, oral and visual communication at an advanced level by using at least one foreign language.
Learning Outcomes
LO-1
Understanding the structure of partially ordered structures and vector lattices.
LO-2
Understanding the structure and extensions of positive operators.
LO-3
Understanding and analyzing the structures of order projections and order-continuous operators.
LO-4
Understanding and analyzing the structure of positive linear functionals, and solving problems involving these.
LO-5
Understanding and analyzing the structures of order homomorphisms and orthomorphisms, and solving problems involving these.
