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Quantitative view on functional analysis 1 - NMMA573

Title:	Kvantitativní pohled na funkcionální analýzu 1
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2024
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	English, Czech
Teaching methods:	full-time

Guarantor:	prof. RNDr. Ondřej Kalenda, Ph.D., DSc.
Teacher(s):	prof. RNDr. Ondřej Kalenda, Ph.D., DSc.

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Annotation -

Quantitative versions of theorems from functional analysis and of properties of Banach spaces. Elective course for Master and PhD students.

Last update: Pyrih Pavel, doc. RNDr., CSc. (10.05.2024)

Syllabus -

Quantitative versions of notions and theorems on Banach spaces and operators between them. For example, the following topics will be addressed:

1) Measures of non-compactness of sets and operators, a quantitative version of Schauder's theorem

2) Measures of weak non-compactness of sets - comparison, their equivalences and non-equvivalences, quantitative versions of Eberlein-Šmulyan and James theorems.

3) Measures of weak non-compactness of operators, quantification of the Gantmacher theorem

4) Quantitative version of Krein's theorem

5) Etc.

Last update: Kalenda Ondřej, prof. RNDr., Ph.D., DSc. (16.05.2024)