Module MA3422: Functional Analysis II
- Credit weighting (ECTS)
- 5 credits
- Semester/term taught
- Hilary term 2016-17
- Contact Hours
- 11 weeks, 3 lectures including tutorials per week
- Lecturer
- Prof. Richard Timoney
- Learning Outcomes
-
On successful completion of this module, students will be able to:
- give the appropriate definitions, theorems and proofs concerning the syllabus topics, including topics related to weak toploogies, compactness, Hahn-Banach theorem, reflexivity;
- solve problems requiring manipulation or application of one or more of the concepts and results studied;
- formulate mathematical arguments in appropriately precise terms for the subject matter;
- apply their knowledge in mathematical domains where functional analytic techniques are relevant.
- Module Content
-
- Hilbert spaces:
- Definition and examples. Orthonormal bases. Parallelogram Identity. Spaces of operators or functionals. Dual of a Hilbert space. Algebra of operators.
- Major theorems:
- Closed graph theorem, uniform boundedness principle, Hahn-Banach theorem.
- Dual spaces:
- Canonical isometric embedding in double dual, reflexivity, examples of reflexive and non-reflexive spaces.
- Weak topologies and Tychonoff's theorem:
- Locally convex topological vector spaces. Weak and weak*-topologies.
For further information refer to the module web pages.
- Module Prerequisite
- MA3421
- Assessment Detail
- This module will be examined in a 2 hour examination in Trinity term. Continuous assessment will contribute 15% to the final grade for the module at the annual examination session.