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We would like to study the structure of Banach spaces, spaces of continuous functions, C* algebras and their relationship. Main topics will include quantitative properties of Banach spaces, decompositions of Banach spaces to smaller subspaces, descriptive properties of the weak topology, James' boundaries of compact convex sets, Baire classes of strongly ane functions, noncommutative Choquet theory, weakly compact sets and spaces they generate, problems of Banach-Stone type for spaces of continuous functions, uniformly continuous functions and ane functions, various types of universal Banach spaces, existence of fixed points and approximate fixed points, noncommutative measure theory, structures on the set of all abelian subalgebras of a C* algebra and a Jordan algebra, representations of operator algebras using weights and completely positive maps, new types of orders on operators. We would like to pay special attention to mutual influence of particular structures and to subsequent connecting of di erent areas of functional analysis and clarifying their mutual relationships.
Main investigator:
Kalenda Ondřej
IM leaders:
Participating institutions:
Institute of Mathematics, AS CR,
Czech Technical University. Faculty of Electrical Engineering. Department of Mathematics, ČVUT FEL,
Mathematical and Physical Faculty of the Charles University, Prague, MFF UK, Prague
IM team members:
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Kopecká Eva |
Kubiś Wiesław |
