Topics in Functional Analysis

Course Description

A generalization of the main notions and concepts of analysis, geometry and algebra. Topics include operators (functions), metric and topological spaces, complete spaces, completion of metric spaces, contraction mapping principle, separable spaces, compactness of sets and criteria of compactness in a metric spaces, linear spaces and linear operators, linear normed spaces, finite spaces and subspaces, abstract Hilbert spaces, linear operators in linear normed spaces, space of linear operators.

Learning Outcomes

  • Evaluate operators, metric spaces.
  • Prove the Contraction Mapping Theorem.
  • Elaborate the main concepts of the compactness.
  • Explore the properties of linear spaces and linear operators.
  • Explore the Banach spaces.
  • Investigate Hilbert spaces.
  • Elaborate the theorem on inverse operators and its applications.

Prerequisites

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