Faculty of Mathematics and Physics

Functional Analysis 1

Information in Student Information System


Organization of the course


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


Recommended literature


Lecture notes


Credit requirements (including overview of results)


Content of the lectures and classes


Conditions from exams


Overview of exam results

Recommended literature

The literature recommended in SIS is the following:
[1] Rudin, W.: Functional analysis. Second edition, McGraw-Hill, Inc., New York, 1991
[2] Meise R. and Vogt D. : Introduction to functional analysis, Oxford University Press, New York, 1997


More precisely:

The first topic, i.e., topological vector spaces and weak topologies approximately corresponds to Chapters 1-3 of [1]. This is not exact, the book contains some additional material (for example, Chapter 2 is presented in a more general setting) and, conversely, something is only briefly mentioned (polar calculus). One can also use Chapter 3 of the book M.Fabian et al.: Banach Space Theory, Springer 2011.


The second topic, elements of vector integration, is not covered by [1] and [2]. The standard literature includes the book J.Diestel and J.J.Uhl: Vector measures, Mathematical Surveys and Monongraphs 15, American Mathematical Society 1977, sections III.1-III.3. Another approach can be found for example in the book R.R.Ryan: Introduction to tensor products of Banach spaces, Springer 2002, in the sections 2.3 and 3.3.


The third topic, i.e., Banach algebras and spectral theory, approximately corresponds to Chapters 10-12 of [1]; Chapters 17 and 18 of [2] are related as well.