Functional calculus and \(*\)-regularity of a class of Banach algebras. II (Q2506414)

The authors define a Banach \(*\)-algebra \(L^1_Q(G; A)\) for a \(C^*\)-dynamical system \((A, G, \alpha)\) which is bigger than \(L^1(G;A)\) (both are the same if \(A\) is finite-dimensional) and is independent on covariant representations. They prove that \(L^1_Q(G; A)\) is \(*\)-regular if \(G\) has polynomial growth. This result extends several results which were proved in Part~1 [\textit{C.\,W.\,Leung} and \textit{C.\,K.\,Ng}, Proc.\ Am.\ Math.\ Soc.\ 134, No.\,3, 755--763 (2006; Zbl 1096.46029)].