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Grantor: Czech Science Foundation

**Objectives:**

We wish to investigate the structure of Banach spaces, C*-algebras and Jordan algebras and their relationship. Main topics include quantitative approach to Banach spaces, various methods of separable reduction, decompositions of Banach spaces to smaller subspaces, integral representation of affine Baire functions, descriptive properties of weak topologies, small sets in Banach spaces and Polish groups, universal spaces in various categories of Banach spaces, operators and their numerical ranges, structure of abelian subalgebras of a C*-algebra, of associative subalgebras of a Jordan algebra and related structures, different types of order in operator algebras, representation of morphisms on various substructures of operator algebras, Bell's inequalities and quantum correlations. We wish to focus especially on those problems where the mentioned areas intersect each other and by solving them to contribute to clarification of connections among various areas of functional analysis.

IM leader :

Main investigator:

**Kalenda** Ondřej

IM team members:

Kurka Ondřej |
Müller Vladimír |

Participating institutions:

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

Institute of Mathematics, Czech Academy of Sciences