The well known Gelfland-Naimark theorem enables us to represent a complex commutative C*-algebra as a full algebra of complex valued functions defined on its set of primitive ideals which is called the structure space of the algebra. In is thesis we are concerned with the generalization of this type of representation theorem to non-commutative rings and algebras. In order to prove the Gelfand-Naimark theorem, we needed the Stone-Weierstrass theorem to enable us to show that a subalgebra is actually equal to a full algebra of functions. We shall see that in order to represent a non-commutative algebra as a set of functions taking values in a variable range, we shall need a suitable type of Stone-Weierstrass theorem. This thesis can therefore be considered as an illustration of the application of Stone-Weierstrass type argunents to the theory of C*-algebra representations.

Reference:

Hacking, S. 1970. Representation of non-commutative topological algebras. University of Cape Town.

Hacking, S. M. (1970). Representation of non-commutative topological algebras. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/22297

Hacking, Susan Margaret. "Representation of non-commutative topological algebras." Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1970. http://hdl.handle.net/11427/22297

Hacking SM. Representation of non-commutative topological algebras. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1970 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/22297