Lorentz Center - Operator Structures and Dynamical Systems from 21 Jul 2008 through 25 Jul 2008
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    Operator Structures and Dynamical Systems
    from 21 Jul 2008 through 25 Jul 2008

 
This workshop is an official satellite of the fifth European Congress of Mathematics in Amsterdam in the preceding week
This workshop is an official satellite of the fifth European Congress of Mathematics in 
Amsterdam in the preceding week. 
 
Many dynamical systems are accompanied by an operator structure which encodes 
essential traits of the dynamics. The principal aim of this workshop is to enhance the 
exchange of knowledge and ideas between researchers from various countries, 
research groups and levels of seniority, who are all interested in the relation between 
dynamical systems and the attached operator structures, as well as to facilitate 
establishing new collaborations between these researchers.
 
A well known instance of the above situation is that of a topological group acting on a 
compact Hausdorff space via homeomorphisms. One can then form the associated 
crossed product C*-algebra, which is the counterpart of the crossed product von 
Neumann algebra associated with a group of measurable transformations. As is well 
known, the associated von Neumann algebra carries relevant information about the 
measurable system, and likewise the associated C*-algebra carries information 
about the topological system. Many results have been brought to light which relate 
the structure of the crossed product and the dynamical properties of the topological 
system. This interplay between topological dynamical systems and C*-algebras has 
been a stimulus for the development of the theory of crossed products of C*-algebras 
in the early days and is still an area of active research.
 
The above is a special case of a more general setting where a group acts on a possibly 
noncommutative C*-algebra rather than on the continuous functions on a compact space, 
in which case it is also possible to construct a crossed product C*-algebra. The general 
theory of such algebras is well established and has significant bearing on the interplay 
between topological dynamical systems and the associated crossed product C*-algebras. 
Yet is not always possible to obtain the more detailed results which can sometimes be 
given in the commutative setting, simply by specialising the general theory, or to provide 
the most efficient and general proofs in that context. Hence here the general and special 
viewpoint supplement one another.
 
Apart from these C*-algebras associated with invertible dynamics (be it abstract or 
topological) several other classes of operator structures are under current research: 
analytic crossed products, C*-algebras associated with non-invertible dynamics and 
transfer operators, Banach algebra crossed products corresponding to a Banach 
algebra dynamical system, etc. In this workshop researchers in all these areas are 
expected to be present, both from the general theory of such algebras and from the 
interplay with topological dynamics when this is applicable.
 
We welcome further contributions in this vein, relating operator structures and dynamical 
systems, as well as applications in other disciplines. 

 



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