Faculty of Mathematics and Physics

Functional Analysis 2

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Content of the course, expected knowledge and connections to other courses


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Content of the course, expected knowledge and connections to other courses

Functional analysis 2 is an advanced course designed mainly for master students of mathematical analysis. This course is a direct continuation of the course Functional Analysis 1 (NMMA401) which itself is already an advanced master course.


Basic topics of the course are the following:

  • Unbounded operators on a Hilbert space
  • Locally convex topologies - advanced topics


The first topic is a direct continuation of Chapters VIII and IX from Functional Analysis 1. The notions like spectrum, spectral measure, spectral decomposition will be studied in a more general context on unbounded operators.


The second topic is a continuation of Chapters V and VI from Functional Analysis 1. It deals with further natural locally convex topologies, their description, comparison and deeper properties and further results on weak compactness.


How to continue?

There are many further courses devoted to functional analysis and itns applications, e.g.:

  • Partial differential equations 1,2 (NMMA405, NMMA406) - applications of functional analysis to studying the solutions of equations, it uses knowledge from the Introduction to functional analysis and, among others, from the second area of this course
  • Diferential equations in Banach spaces (NMMA440) - some notions and results from the third area and their generalizations are used
  • Topological methods in functional analysis 1,2 (NMMA435, NMMA436) - a deeper study of weak topologies and of differentiability of convex functions on Banach spaces
  • Introduction to the theory of approximations 1,2 (NMMA565, NMMA566) - applications of functional analysis to the study of approximations, i.e., of the nearest points
  • Introduction to the theory of interpolations 1,2 (NMMA533, NMMA534) - applications of functional analysis to the study of various function spaces
  • Nonlinear functional analysis 1, 2 (NMMA501, NMMA502)