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

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
[5] 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 [2].

The second topic, 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.

The third topic, i.e., Banach algebras and spectral theory, approximately corresponds to Chapters 10-12 of [1]; Chapters 17 and 18 of [5] are related as well.