Functional Analysis 1Information in Student Information System Content of the course, expected knowledge and connections to other courses Credit requirements (including overview of results) Content of the lectures and classes |
Recommended literatureThe literature recommended in SIS is the following: 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. |