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Abstract:
By the theorems of Gelfand and Gelfand-Naimark we know that we can represent commutative Banach algebras and commutative C*-algebras respectively by spaces of continuous functions. For non-commutative C*-algebras we have the GNS-construction.
In our paper we will show that under mild assumptions a non-commutative C*-algebra can be represented by a space of continuous mappings. This can be done just in the same way as in the commutative case.