Functional calculus and ∗-regularity of a class of Banach algebras II

In this article, we define a natural Banach ∗-algebra for a C∗-dynamical system (A,G,α) which is slightly bigger than L1(G;A) (they are the same if A is finite-dimensional). We will show that this algebra is ∗-regular if G has polynomial growth. The main result in this article extends the two main results in [C.W. Leung, C.K. Ng, Functional calculus and ∗-regularity of a class of Banach algebras, Proc. Amer. Math. Soc., in press].