# 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 sucessful 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.