Language of Instruction

English

Level of Course Unit

First Cycle

Department / Program

MATHEMATICS

Mode of Delivery

Face to Face

Type of Course Unit

Elective

Objectives of the Course

To introduce students with basic notations and concepts related with the abstract spaces and linear operators. To show the use of theoretical knowledge in solving some applied problems. To motivate students to do research and use different literature when learning the course. To give elementary background for more advanced study in Functional analysis.

Course Content

Metric spaces. Banach and Hilbert Spaces. Linear Operators on Normed Spaces, Bounded and Compact Operators. Spaces of Linear Operators and Convergence. Fundamental Theorems for Normed and Banach Spaces: HanhBanach Theorem, Uniform Boundedness Theorem, Open Mapping Theorem, Closed Graph Theorem. Linear Functionals on Hilbert Spaces and Riesz Representation Theorem. Adjoint, Selfadjoint, Unitary and Normal Operators. Spectrum and Resolvent of an Operator. Spectral Properties of Bounded and Compact Operators. Unbounded Operators and Their Basic Properties.

Course Methods and Techniques


Prerequisites and corequisities

None

Course Coordinator

None

Name of Lecturers

ŞİRİN ATILGAN BÜYÜKAŞIK

Assistants

None

Work Placement(s)

No

Recommended or Required Reading
Resources

Walter Rudin, “Functional Analysis”, McGrawHill,Inc. E. Kreyszig, “Introductory Functional Analysis with Applications”, JohnWiley &Sons. L. Debnath, P. Mikusinski, “Introduction to Hilbert spaces with Applications”, Third edition. I. Gohberg, S. Goldberg, “Basic Operator Theory”, Birkhauser. A. N. Kolmogorov, S.V. Fomin, “Introductory Real Analysis”, Dover Publications,INC.









