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Infinite Dimensional Vector Spaces

Key information

  • Module code:

    7CCMMS05

  • Level:

    7

  • Semester:

      Autumn

  • Credit value:

    15

Module description

Syllabus

Various topics to be discussed include metric spaces, continuous maps, normed spaces, completeness, bounded linear maps, Banach-Steinhaus theorem, compactness, Stone-Weierstrass theorem, Hahn-Banach theorem, the dual space. Instruction is by formal lectures.

Prerequisites

A rigorous analysis module (such as Real Analysis or similar) and some knowledge of linear algebra. You are advised to have taken 226A/B Metric Spaces and Topology 

Assessment details

2 hr written examination

Semester 1 only students will be set an alternative assessment in lieu of in-person exams in January.

Full year students will complete the standard assessment.

Educational aims & objectives

To discuss some fundamental aspects of functional analysis

Teaching pattern

Two hours of lectures and one hour of tutorial per week throughout the term

Subject areas

Department

Module description disclaimer

King’s College London reviews the modules offered on a regular basis to provide up-to-date, innovative and relevant programmes of study. Therefore, modules offered may change. We suggest you keep an eye on the course finder on our website for updates.

Please note that modules with a practical component will be capped due to educational requirements, which may mean that we cannot guarantee a place to all students who elect to study this module.

Please note that the module descriptions above are related to the current academic year and are subject to change.