THEOREM. (Dauns-Hofmann), Let A be a C^*-algebra with identity and X the space of maximal ideals of the center of A with the hull-kernel topology. Then A is isometrically *-isomorphic to the C^{*}-algebra of all continuous sections r(\pi) of a C^{*}-bundle \xi=(\pi, \mathrm{B}, \mathrm{X}) over \mathrm{X}. The fiber above m \in X is the quotient Z^{*}-algebra A / mA, the isometric *-isomorphism is the Gelfand representation x \rightarrow x^{\wedge}, where x^{\wedge}(m)=x+mA, and the norm of x^{\wedge} is given by
$$
\left\|x^{\wedge}\right\|=\sup \left(\left\|x^{\wedge}(m)\right\|: m \in X\right)
$$
Further, the real-valued map m\to\left\|x^{\wedge}(m)\right\| on x is upper-semf continuous for each x \in A.
Although the original proof of Dauns and Hofmann was quite involved technically, a simple, self-contained, proof, using ldeas of J,
Varela [1], is available in the book by M, J. Dupre and R.M.Gillette [1], Another proof, using category theory and sheaves, has
been given by C. J. Mulvey mul. The theorem is also treated in the book by G. K. Pedersen [1], pp. 106-108].