Banach spaces and their generalizations (locally convex spaces) are one of the main tool in modern analysis. They serve as a framework for differential calculus and solving differential equations (including partial ones) and provide a great variety of questions concerning their structure. We plan to focus on topological, geometrical and algebraic structures of these spaces and interaction between these structures. The main areas include topological characterizations of important classes of Banach spaces, dual classes of compact spaces, spaces of continuous functions, properties of compact convex sets, differentiability of convex functions, relations between different weak topologies, special subsets of Banach spaces, descriptive properties of sets and operators. The nature of the project is a theoretical research in the above mentioned areas. The results will be published in scientific journals and presented at international conferences.
IM leaders:
Participating institutions:
Institute of Mathematics, AS CR,
Mathematical and Physical Faculty of the Charles University, Prague, MFF UK, Prague
IM team members:
|
Hájek Petr |
Kolář Jan |
