Faculty of Mathematics and Physics

Functional Analysis 2

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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:

  • Bounded and unbounded operators on a Hilbert space
  • Spectral measures and decompositions
  • Locally convex topologies - advanced topics


The first topic is a direct continuation of Chapter IV from Functional Analysis 1. It is devoted to a more detailed study of the spectrum for bounded operators and to the notion of spectrum in a more general context on unbounded operators. The second topic is a continuation of the first one - it deals with the measurable calculus for bounded normal operators (this is a generalization of the continuous functional calculus from Chapter IV), spectral measures and spectral decompositions for both bounded and unbounded operators.


The third topic is a continuation of Chapters I and II 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), Diferential equations in Banach spaces (NMMA440) - applications of functional analysis to studying the solutions of equations
  • 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)