TY - JOUR
ID - 44047
T1 - The closure of ideals of $ell^1(Sigma)$ in its enveloping $mathrm{C}^*$-algebra
JO - Advances in Operator Theory
JA - AOT
LA - en
SN -
A1 - Jeu, Marcel de
A1 - Tomiyama, Jun
Y1 - 2018
PY - 2018/01/01
VL - 3
IS - 1
SP - 42
EP - 52
KW - Primary 46K99
KW - Secondary 46H10, 47L65, 54H20
DO - 10.22034/aot.1702-1116
N2 - If $X$ is a compact Hausdorff space and $sigma$ is a homeomorphism of $X$, then an involutive Banach algebra $ell^1(Sigma)$ of crossed product type is naturally associated with the topological dynamical system $Sigma=(X,sigma)$. We initiate the study of the relation between two-sided ideals of $ell^1(Sigma)$ and ${mathrm C}^ast(Sigma)$, the enveloping $mathrm{C}^ast$-algebra ${mathrm C}(X)rtimes_sigmamathbb Z$ of $ell^1(Sigma)$. Among others, we prove that the closure of a proper two-sided ideal of $ell^1(Sigma)$ in ${mathrm C}^ast(Sigma)$ is again a proper two-sided ideal of ${mathrm C}^ast(Sigma)$.
UR - http://www.aot-math.org/article_44047.html
L1 - http://www.aot-math.org/pdf_44047_f65a8f1062ea283744db5848a9363ba9.html
ER -