

Algebras in Analysis
February 15, 2019 18:05–19:35, Moscow, Lomonosov Moscow State University, room 1320.






The DaunsHofmann theorem
B. I. Nazarov^{} 
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Abstract:
The GelfandNaimark theorem identifies a commutative unital C*algebra A with C(Spec A). This leads to a natural conjecture that each noncommutative C*algebra A corresponds to an algebra of operatorvalued functions on Prim A.
This was the original motivation for the development of C*bundle theory. The results of this program are not completely satisfactory. Noncommutative generalizations of the GelfandNaimark theorem were proved only for rather narrow classes of C*algebras. On the other hand, some progress has been made, and the DaunsHofmann theorem is a good illustration. The theorem states that each C*algebra is a module over the algebra of continuous functions on the primitive ideal space.
In our talk, we discuss the structure of Prim A and prove the DaunsHofmann theorem

