Mathematics
MA482: Functional Analysis (5 ECTS)
This course introduces the theory of Linear Functional Analysis. Topics include Banach Spaces, Bounded Linear Operators, Dual Spaces, Hilbert Spaces, Orthogonal Complements and Direct Sums, Representation of Functionals on Hilbert Spaces and the Hilbert-Adjoint Operator.
Taught in Semester(s) 2. Examined in Semester(s) 2.
Workload: 116 hours (24 Lecture hours, 8 Tutorial hours, 84 Self study hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Understand the fundamentals in Normed Spaces, Linear Operators and Dual Spaces.
- Understand the fundamentals of Inner Product Spaces, Direct Sums and Hilbert-Adjoint Operators.
- Solve problems associated with Banach Spaces, Continuous Linear Operators, Normed Spaces of Operators and Dual Spaces.
- Solve problems associated with Inner Product Spaces, Orthogonal Complements, Orthonormal Sets and Sequences, Functionals on Hilbert Spaces and the Hilbert-Adjoint Operator.
Indicative Content
This course introduces the theory of Linear Functional Analysis. The material covered includes Normed Spaces, Continuous Linear Operators, Normed Spaces of Operators, Dual Spaces, Inner Product Spaces, Orthogonal Complements and Direct Sums, Orthonormal Sets and Sequences, Representation of Linear Functionals on Hilbert Spaces and the Hilbert-Adjoint Operator.
Module Resources
- Introductory Functional Analysis and Applications by Edwin Kreyszig, John Wiley & Sons.
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