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Module MA3422: Functional analysis II

Credit weighting (ECTS)
5 credits
Semester/term taught
Hilary term 2012-13
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, commutative Banach algebras;
  • 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
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.
General topology:
Product topology. Tychonoff theorem on compactness of (general) product space
Weak and weak*-topologies:
Compactness of the unit ball of the dual in the weak*-topology.
Gelfand theory of commutative Banach algebras:
Maximal ideal space. Gelfand transform.

For further information refer to the module web pages.

Module Prerequisite
MA3421
Assessment Detail
This module will be examined jointly with MA3421 in a 3-hour examination in Trinity term, except that those taking just one of the two modules will have a 2 hour examination. Continuous assessment will contribute 15% to the final grade for the module at the annual examination session.