In this short article, we will give several results concerning closed invariant ideals of crossed products using some "topological arguments".

By giving an interesting characterisation of amenable multiplicative unitaries, we show, in a very simple way, that bicrossproducts of amenable locally compact groups are both amenable and coamenable.

Suppose that (A, G, α) is a C -dynamical system such that G is of polynomial growth. If A is finite dimensional, we show that any element in K (G; A) has slow growth and that L1 (G,A) is *-regular. Furthermore, if G is discrete and π is a "nice representation" of A, we define a new Banach-algebra l1 (G,A) which coincides with l1 (G; A) when A is finite dimensional. We also show that any element in K (G; A) has slow growth and l1 (G,A) is-regular.

We will prove a result concerning the inclusion of non-trivial invariant ideals inside non-trivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of locally compact groups on C*-algebras.

In this paper, we will give a natural definition for morphisms between multiplicative unitaries. We will then discuss some equivalences of this definition and some interesting properties of them. Moreover, we will define normal sub-multiplicative unitaries for multiplicative unitaries of discrete type and prove an imprimitivity type theorem for discrete multiplicative unitaries.