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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.