This paper is divided into
two sections. The first deals with Banach algebra homomorphisms of a von Neumann
algebra A, and extends the Bade-Curtis theory for commutative B∗-algebras to von
Neumann algebras, as well as characterizing the separating ideal in the closure of the
range of the homomorphism. The second section concerns homomorphisms of
B∗-algebras; the chief result being the existence of an ideal ℐ with cofinite closure
such that the restriction of the homomorphism to any closed, two-sided ideal
contained in ℐ is continuous.
