If X X
is a compact Hausdorff space and σ σ
is a homeomorphism of X X
, then an involutive Banach algebra ℓ 1 (Σ) ℓ1(Σ)
of crossed product type is naturally associated with the topological dynamical system Σ=(X,σ) Σ=(X,σ)
. We initiate the study of the relation between two-sided ideals of ℓ 1 (Σ) ℓ1(Σ)
and C ∗ (Σ) C∗(Σ)
, the enveloping C ∗ C∗
-algebra C(X)⋊ σ Z C(X)⋊σZ
of ℓ 1 (Σ) ℓ1(Σ)
. Among others, we prove that the closure of a proper two-sided ideal of ℓ 1 (Σ) ℓ1(Σ)
in C ∗ (Σ) C∗(Σ)
is again a proper two-sided ideal of C ∗ (Σ) C∗(Σ)
.Analysis and Stochastic
