Ondrej Kalenda

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
(and statistical data on homeworks)

Content of the lectures and classes

Conditions for exams (examination has been finished)

Overview of exam results

Recommended literature

The lecture notes available (here, to be completed) form the basic source.

The literature recommended in SIS is the following:
[1] Rudin, W.: Functional analysis. Second edition, McGraw-Hill, Inc., New York, 1991
[2] M.Fabian et al.: Banach Space Theory, Springer 2011
[3] J.Diestel and J.J.Uhl: Vector measures, Mathematical Surveys and Monongraphs 15, American Mathematical Society 1977
[4] R.R.Ryan: Introduction to tensor products of Banach spaces, Springer 2002

More precisely:

Chapters V and VI, i.e., locally convex spaces and weak topologies approximately corresponds to Chapters 1-3 of [1]. This is not exact, the book works in a more general setting (for example Chapter 2 and, in general, the text works with general topological vector spaces) and, conversely, something is only briefly mentioned (polar calculus). One can also use Chapter 3 of book [2].

Chapter VII, the theory of distributions, is more than covered by chapters 6 and 7 of [1].

The topic of Chapter VIII, elements of vector integration, is addressed for example in sections III.1-III.3 of [3] Another approach can be found for example in the book [4], in sections 2.3 and 3.3.

Chapter IX, compact convex sets, is covered by Sections 3.8 and 3.9 of [2].