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Functional Analysis II: Course Outline (MAT 456)

In modern introductory texts to functional analysis, the subject is seen as the study of vector spaces endowed with a topology, in particular infinite-dimensional spaces.

Course Objective

At the end of this course the students will be able to understand fundamental theorems in functional analysis and their applications. Further they would be able to understand basic notion of spectral theory and some theorems.

Course Contents

  • The Hahn-Banach theorem,
  • Principle of uniform boundedness,
  • Open mapping theorem,
  • Closed graph theorem,
  • Weak topologies and the Banach-Alouglu theorem,
  • Extreme points and the Klein-Milman theorem,
  • The dual and bidual spaces, Reflexive spaces,
  • Compact operators, Spectrum and eigenvalues of an operator,
  • Elementary spectral theory. 

Text Books

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