Algebraic properties of the Mikusiński convolution algebra (Q5932735)

Let \(\mathcal M\) be Mikusiński's convolution algebra of all continuous, complex valued functions over \([0,\infty)\), and \(\mathcal M^1\) its extension by unity. The authors investigate the ideal structure of \(\mathcal M\) and \(\mathcal M^1\), and give new proofs concerning the fact that \(\mathcal M\) is a Jacobson radical algebra, and concerning the solutions of certain operator equations.