University of Galway

Course Module Information

Course Modules

Semester 2 | Credits: 5

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.

Learning Outcomes
  1. Understand the fundamentals in Normed Spaces, Linear Operators and Dual Spaces.
  2. Understand the fundamentals of Inner Product Spaces, Direct Sums and Hilbert-Adjoint Operators.
  3. Solve problems associated with Banach Spaces, Continuous Linear Operators, Normed Spaces of Operators and Dual Spaces.
  4. Solve problems associated with Inner Product Spaces, Orthogonal Complements, Orthonormal Sets and Sequences, Functionals on Hilbert Spaces and the Hilbert-Adjoint Operator.
Assessments
  • Written Assessment (75%)
  • Continuous Assessment (25%)
Teachers
Reading List
  1. "Introductory Functional Analysis with Applications" by E. Kreyszig
    ISBN: 9788126511914.
    Publisher: Wiley Publishing
The above information outlines module MA482: "Functional Analysis" and is valid from 2015 onwards.
Note: Module offerings and details may be subject to change.