The Stone-Čech compactification of Prim A

Abstract

For a C*-algebra A, we give simple proofs of the following: Cb (Prim A) is isomorphic to the centre ZM(A) of the multiplier algebra, Cb (Prim A) is isomorphic to C (Prim M(A)) and Prim ZM(A) is the Stone-Čech compactification of Prim A.