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Grantor: Czech Science Foundation (GAČR)

**Objectives**:

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 dierent areas of functional analysis and clarifying their mutual relationships.

IM leader :

Main investigator:

**Kalenda** Ondřej

IM team members:

Kolář Jan Kopecká Eva |
Kubiś Wiesław |

Participating institutions:

Faculty of Mathematics and Physics, Charles University in Prague, **Coordinator**

Institute of Mathematics, Czech Academy of Sciences

Faculty of Electrical Engineering, Czech Technical University